We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures. For the mean-field Transformer model with self-attention and affine feed-forward layers, we prove that Gaussian distributions remain exactly Gaussian along the induced flow. This invariance reduces the infinite-dimensional measure dynamics to a finite-dimensional bilinear control system governing the evolution of the mean and covariance, reformulates the expressive capacity of Transformers as a reachability problem for prescribed Gaussian moments, and reveals a novel connection with Riccati-type equations from classical filtering and control. For time-varying controls, we prove exact finite-time reachability of any target Gaussian distribution whose covariance matrix has the same rank as the initial one, this rank constraint being an intrinsic invariant of the dynamics. For time-invariant parameters, we derive explicit spectral conditions leading either to asymptotic stability toward positive-definite equilibria or to finite-time blow-up of the covariance. Numerical experiments complement the theory by showing that practical Transformers with Gaussian inputs remain close to moment-matched Gaussian distributions through early and intermediate layers, while Transformers with prescribed attention matrices reproduce the predicted covariance regimes: bounded evolution in stabilizing configurations and blow-up in destabilizing ones.

We introduce the Laplace-Fourier Neural Operator (LFNO), a unified framework for modeling dynamical systems across transient and steady-state regimes by integrating the spectral advantages of Laplace and Fourier Neural Operators. LFNO employs a dual-branch architecture that explicitly decomposes system dynamics into transient and steady-state components. We evaluate LFNO on nine benchmarks, including three ODE systems (Duffing, Lorenz, and Pendulum) and six PDE systems (Euler-Bernoulli beam, Heat, Reaction-diffusion, Brusselator, Burgers, and Navier-Stokes). LFNO significantly outperforms existing operators on ODE systems, where transient dynamics dominate, and consistently surpasses LNO while achieving performance competitive with FNO on PDE benchmarks. Furthermore, LFNO offers improved stability and physical interpretability through its component-wise decomposition. These results demonstrate that LFNO provides a robust and unified approach for learning complex dynamical systems across multiple temporal scales.

Analyzing attention weights has become a standard approach for interpreting the information flow of Large Language Models (LLMs). However, this approach has significant limitations as it neglects the geometric properties of the value vectors being aggregated. To address this gap, we introduce \emph{Contribution Weights}, a projection-based metric that quantifies a token's influence by accounting for it's attention weight, value magnitude, and directional alignment with the layer output. We demonstrate that contribution weights provide a more faithful measure of token importance, consistently outperforming attention-based metrics in identifying semantically critical tokens across different decoder-only models, tasks, and datasets. Further, our metric enables novel mechanistic analysis of \emph{attention sinks}. While previous work characterized sinks as passive repositories for excess attention, we reveal they serve an active functional role, suppressing information through a convex relationship between sink rate and output norm, stabilizing representations by opposing the semantic drift of low-confidence tokens.

Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities. Despite significant recent strides in spatio-temporal modeling, existing approaches often fail to explicitly model the coupling relationships between different modality variables. Accurate MoSTF is challenging, as it requires modeling (1) temporal dynamic heterogeneity under exogenous influences and (2) heterogeneous spatial dependencies alongside complex cross-variable couplings. To address these challenges, we propose the Dual-Domain Spectral Filtering Network (DSFNet). Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns and explicitly model the relationships between variables. Unlike graph-based message passing or dense attention over node-modality pairs, DSFNet factorizes space-modality interactions into feature-domain and spatial-domain spectral operators, enabling scalable modeling of nonlocal dependencies and cross-modality couplings. Furthermore, we introduce an external gating mechanism to adaptively regulate temporal dynamics under external influences. We validate our method through extensive experiments on five representative real-world traffic datasets. Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets. The results demonstrate that DSFNet significantly outperforms existing state-of-the-art baselines in accuracy while exhibiting efficiency and robustness.

The autoregressive nature of large language models (LLMs) remains a significant bottleneck for inference, particularly in complex agentic workloads. While speculative decoding (SD) accelerates inference, current approaches rely on static drafting paradigms, utilising either autoregressive drafting models for reasoning or diffusion-based parallel drafting models for structured outputs. We empirically find that drafting accuracy fluctuates dramatically within a single sequence, leaving significant performance unrealised by static paradigms and coarse-grained routing. To address this volatility, we introduce WhiFlash, the first cross-paradigm SD method that unifies autoregressive and diffusion-based parallel drafting under a single token-level controller. WhiFlash adopts a fine-grained routing mechanism that employs either a lightweight entropy-based or a learned neural policy, both parametrised to provide a tunable balance between expected token gain and latency. To make high-frequency switching computationally viable, we introduce novel cache-management optimisations, Lazy Catch-up and KV-only Prefill, reducing switching overhead to below 7% of per-round latency. By capitalising on the complementary strengths of fundamentally distinct drafting architectures, WhiFlash achieves significantly higher acceptance lengths, yielding category-specific throughput gains of up to 69.6% over the state-of-the-art autoregressive EAGLE-3 and 37.3% over the diffusion-based DFlash.

When a language model trains on its own verified outputs, does it acquire capability beyond its base, or merely get better at expressing capability the base already had? We make the question decidable with a teacher-free "constellation" -- a generator, a learned critic, and a free exact verifier -- on a FlashFill-style "trapdoor" DSL, where verified (problem, solution) pairs are cheap to synthesize, hard to invert, and free to check exactly. Everything runs on one 4-bit Qwen3-4B on a single 24 GB GPU, with no model in the loop larger than the base. We report three findings. (i) Critic-guided selection beats verifier-filtered best-of-$k$ by $+9.1$ pp ($6/6$ seeds), with the entire gain localized to tasks where candidates disagree on held-out inputs. (ii) Per-round STaR self-training raises the ceiling but never accelerates -- the gain tracks remaining headroom and decelerates across $K=4$ independent training trajectories. (iii) The domain has no clean zero-capability frontier, so the usual "$0\% \to$ climb $=$ emergence" test is invalid here. A measured pass@$K$ crossover settles the diagnosis: the trained model wins at the operating budget (pass@$8$) but the base overtakes it at a large budget (pass@$64$) on every trajectory, so self-training concentrates probability mass rather than expanding reach. This is amplification, not compounding. ($K=4$ is indicative, not yet a robust across-trajectory CI.)

Pipeline parallelism is essential for training large neural networks, but existing schedules trade off throughput, memory, and optimization consistency. Synchronous pipelines preserve forward/backward weight consistency but suffer from bubbles; asynchronous pipelines remove bubbles but introduce weight-version mismatch, typically requiring weight stashing, prediction, or correction mechanisms. We introduce PACI (Pipeline Asynchronous training with Controlled Inconsistency), a bubble-free asynchronous pipeline method that bounds forward/backward version drift without weight stashing, prediction, additional parameter copies, or global synchronization. The key idea is to use local gradient accumulation as a version-control mechanism: by slowing parameter-version evolution relative to pipeline delay, PACI limits the number of optimizer updates crossed by any micro-batch while preserving steady-state utilization. In GPT-style language-model pretraining, PACI matches the stability and final perplexity of synchronous 1F1B-flush, retains the same peak memory footprint, achieves fully utilized pipeline throughput, and improves training time-to-accuracy by up to $1.69\times$ over the fastest flush baseline. These results show that forward/backward inconsistency need not be eliminated: when explicitly bounded, it can be safely traded for substantial efficiency gains.

Derivative-controlled networks based on ChainzRule (CR) combine cubic polynomial layers with a lightweight forward-mode per-layer Jacobian penalty (DREG). In this second paper of a multi-part series, we evaluate the generalization properties of CR across data regimes. We ablate the shape of the DREG coefficient schedule, demonstrating that the optimal annealing range depends on representation noise. On the Pima Diabetes dataset, CR achieves strong low-data performance and maintains a consistent accuracy advantage over baselines from 5\% to 100\% training data, supported by exceptionally stable gradient tail ratios ($\sim$1.01--1.02 vs. 1.07--1.09 for ReLU networks). Extensions to SST-5 show competitive or superior results in both frozen-embedding and BERT fine-tuned regimes, including outperforming prior BERT baselines despite substantially less training data. These results are statistically significant: CR achieves superior accuracy over the strongest published baselines we could identify on both datasets ($p < 0.05$). These results establish that layer-wise derivative control induces a structural inductive bias toward low-frequency, stable representations that generalizes robustly across tabular and NLP domains, data volumes, and representation qualities. The gradient tail ratio serves as a reliable, label-free diagnostic of generalization capability.

When attention concentrates on a single token, a sink, what is the model actually computing? Attention sinks are ubiquitous in softmax transformers, yet this shared visual signature can hide fundamentally different algorithms. We show that visually similar sink patterns can reflect two distinct mechanisms: {i} adaptive nop, where a head suppresses its update by routing to a null token, and {ii} broadcast, where a sink aggregates and redistributes global information. In that case, sinks serve an analogous role: a safe destination when there is nothing useful to compute. Proposed interventions like gating or registers work because they implicitly target one or the other, revealing a duality between method and assumed mechanism: gating implicitly assumes nop; registers implicitly assume broadcast. Each mechanism leaves distinct traces (nop sinks exhibit negligible value norms; broadcast sinks induce low-rank outputs) which we formalize on synthetic tasks and use to derive practical diagnostics. Applied to pretrained vision transformers, these diagnostics reveal that both mechanisms exist at scale: sinks transition from CLS in early layers to patches in deeper layers, and concentrate in specialized heads. Strikingly, register tokens, designed for broadcast, are repurposed to also serve nop, confirming that neither intervention alone suffices. Combining gating with registers yields complementary gains in stability and performance. Overall, we find that the same attention pattern can reflect two very different computations and effective intervention requires first asking what the model is actually computing.

Token aggregation is a common bottleneck in models that map token representations to sample-level predictions, yet most pooling methods operate only in the original token domain. We propose FLaG, a plug-in aggregation module that transforms token representations with the real FFT, summarizes spectral components with learnable latent queries, applies a channel-wise gate, and reconstructs enhanced time-domain tokens for final pooling. We evaluate FLaG on antimicrobial peptide (AMP) activity prediction with ESM2, image classification with ResNet18 on CIFAR-10 and CIFAR-100, and text classification with RoBERTa on IMDB and GLUE. FLaG achieves its clearest gains on the ESM2-8M antimicrobial peptide tasks and on CIFAR-100, while remaining competitive with strong text baselines on IMDB and GLUE. Then we probe its behavior on the AMP setting with band knockouts, gate summaries, residue perturbations, latent-query readouts, and structure-proxy stratification. We find that low-frequency bands contribute the most overall, and the remaining higher-band pattern is more sample-specific. The gate acts as a broadly shared spectral reweighting stage and the cross-attention patterns are sample-specific with mild query-wise differentiation, and higher-helix peptides exhibit stronger average spectral sensitivity in both bacteria. The supplementary materials, source code and data are released at https://www.healthinformaticslab.org/supp/ and https://github.com/Kewei2023/AMPCliff/tree/FLaG.

Recent advances in Large Language Models (LLMs) have opened new possibilities for time series forecasting by enabling alignment between temporal patterns and pretrained word embeddings. However, most LLM-based methods overlook the heterogeneous nature of time series, where dynamic fluctuations and invariant semantics are entangled. This entanglement introduces spurious correlations during the alignment, as dynamic components act as confounders by simultaneously influencing invariant components and the resulting aligned embeddings. To address this issue, a variable-level alignment framework CVAformer is proposed. CVAformer explicitly disentangles each variable into invariant and dynamic components just before alignment, and applies causal intervention to mitigate the confounding effect of the dynamics. To better support variable-level alignment, CVAformer replaces the standard causal attention in LLMs with a non-causal attention mechanism that captures interactions among variables at each time step. Extensive experiments across long-term, short-term, few-shot, and zero-shot forecasting settings indicate that CVAformer matches or exceeds state-of-the-art performance on most datasets, and in some cases achieves notably better accuracy. Experimental results validate the effectiveness of variable-level alignment and dynamic disentanglement in CVAformer, offering a new perspective for LLM-based time series tasks.

Activation steering provides a lightweight inference-time mechanism for controlling large language models (LLMs) by modifying their internal activation vectors toward desired behaviors. Most existing methods compute a fixed steering direction in the original activation space, typically from pairs of contrastive examples using mean differences, linear probes, or arbitrary separability criteria. While effective to a certain extent, these methods treat behavioral control as a global, linear, additive offset: the same direction is applied across inputs, and behaviors are linearly separable. This can be restrictive when behavioral features vary nonlinearly across the activation space or lie on curved and anisotropic manifolds, where the optimal intervention may be input-dependent. To address this limitation, we propose INNSteer, a nonlinear activation steering framework based on invertible latent transformations. Rather than searching for a better steering vector in the original representation space, INNSteer learns a lightweight invertible neural network $ϕ$ that maps an LLM's activations into a latent space where behavioral classes are more amenable to linear control. At inference time, activations are mapped through $ϕ$, steered in the latent space, and mapped back through the exact inverse transformation $ϕ^{-1}$. This makes a simple latent-space translation become a nonlinear, input-dependent intervention in the original activation space. Across experiment settings on multiple LLM families, scales, behavioral traits, and safety benchmarks, INNSteer consistently improves model control over linear, transport-based, and nonlinear steering baselines while largely preserving generation fluency.

Recently, large time series models (LTSMs) have gained increasing attention due to their similarities to large language models, including flexible context length, scalability, and task generality, outperforming advanced task-specific models. However, prior studies indicate that pre-trained LTSMs may exhibit a poorly conditioned non-convex loss landscape, leading to limited trainability. As a result, direct fine-tuning tends to cause overfitting and suboptimal performance, sometimes even worse than training from scratch, substantially diminishing the benefits of pre-training. To overcome this limitation, we propose Smoothed Full Fine-tuning (SFF), a novel fine-tuning technology. Specifically, we construct an auxiliary LTSM via random initialization to obtain a smoother loss landscape, and then linearly interpolate its weights with those of the pre-trained model to smooth the original landscape. This process improves trainability while preserving pre-trained knowledge, thereby enabling more effective downstream fine-tuning. From an optimization perspective, SFF perturbs sharp minima without significantly harming flat regions, facilitating escape from poor local basins toward smoother and more generalizable solutions. Extensive experiments on benchmark datasets demonstrate consistent improvements across eight representative LTSMs, including Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, and Sundial, on diverse downstream tasks. The code is available at the link: https://github.com/Meteor-Stars/SFF.

Inference-Time Scaling (ITS) has largely succeeded in verifiable domains like math and coding, where cheap verification enables scalable output selection. However, extending ITS to tasks prone to systematic failure - driven by faulty initial assumptions or unmet multidimensional constraints - typically relies on costly external solvers or brittle, model-based verifiers. Our key insight is that the intrinsic statistics of parallel sample sets, specifically length-adjusted tail entropy, provide a robust discriminative signal for solution quality without access to ground truth. Crucially, these statistics serve as a difficulty gate for adaptive compute allocation, dynamically routing problems across scaling regimes. First, Intrinsic Selection (iS) ranks candidates post-hoc, matching consensus-based algorithms across three domains and improving engineering design selection by 20% over pass@1 baselines. Second, Intrinsic Particle Filtering (iPF) generalizes this to step-level resampling, guiding generation toward high-confidence reasoning trajectories to improve pass@1 by 6.1 points on average on hard math problems. Finally, Particle Distillation (dPF) injects privileged guidance via early logit blending and KL-guided resampling, steering generation past systematic reasoning errors to satisfy expert rubrics, yielding up to 26.5% gains on complex clinical responses. Our pipeline applies seamlessly across broad-purpose, domain-specialized, and multimodal architectures, successfully extending ITS to open-ended domains without requiring trained reward models or exact ground-truth verification.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_ϕ$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting representation, finite pathwise stopping times, and a theoretical framework for time-uniform confidence sequences. Simulations support the theory. Backward-coherence regularisation reduces the empirical quasi-martingale total $\hat Q$ by $43$--$58%$, reaches stability $28$--$44%$ earlier than an unregularised RNN, and gives tracking-error recovery consistent with geometric bounds. Additional tests confirm echo-state forgetting rates bounded by $ρ$ and verify the increment-sum tube $R_t$ with $100%$ simultaneous coverage, although $R_t$ is conservative; in practice, the defect-tail proxy $\hat Q_t$ is the more useful monitor. The backward-coherence loss is also equivalent to minimising a Kullback--Leibler divergence in a Gaussian backward model, linking the method to variational inference. Extensions cover $ϕ$-mixing inputs, change-point tracking, and finite-sample concentration. Three real-data studies further validate the approach. On PhysioNet 2012 ICU data, the Reverse Martingale RNN (RMRNN) matches RNN mortality-prediction AUC while reaching stable representations 13 hours earlier. On FRED-MD, it reduces one-month-ahead forecast error by about fourfold under concept drift. On UCI Human Activity Recognition, it maintains lower post-transition tracking error with geometric decay. The guarantees apply under the stated assumptions; universality is not claimed.

While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a layerwise non-uniform training mechanism: downstream classifier weights are driven by dense cross-entropy gradients into a rank-2 equiangular configuration before upstream embeddings fully reorganize, and once this classifier plane forms, backpropagated feature gradients constrain embedding motion to the same plane while weight decay suppresses orthogonal components. Second, after this subspace locking, the induced in-plane dynamics admit an entropy-regularized transport interpretation on $S^1$; combined with modular-addition labels, this reduces embedding formation to phase alignment, whose minimizers are single-frequency characters of $\mathbb{Z}/P\mathbb{Z}$ and hence equal-angle points on a circle. Third, we quantify why this solution prevails over NC: a simplex ETF gains only an $O(1)$ advantage in cross-entropy, whereas the cyclic rank-2 solution enjoys a $Θ(K)$ advantage under Schatten or weight-decay surrogates, yielding a critical threshold $λ_{\mathrm{crit}} = Θ(1/K)$. Our results explain both why classifier weights move first and why embeddings subsequently align with them, showing that grokking on modular arithmetic is governed not by maximal separation alone but by a task-structured trade-off between separation, symmetry, and complexity.

Two-stage post-training -- a Stage-1 warm-start (supervised fine-tuning, SFT, or on-policy distillation, OPD) followed by Stage-2 reinforcement learning (RL) -- is increasingly used for vision-language models (VLMs). We ask what Stage-1 actually controls in a small-data study using Qwen2.5-VL-7B with a same-modality 72B VLM teacher for OPD. First, the three warm-starts reach a narrow $53$--$54\%$ band on Geometry3K internal validation, consistent with the narrow range reported by recent specialized methods; this setup provides little evidence that Stage-1 changes the in-domain endpoint. Second, a matched-recipe, early-stopped SFT improves out-of-domain MathVista by $+2.1$ points, reversing the $-9.5$-point drop of an over-trained variant. The clearest difference is the \emph{entropy regime}: OPD enters RL with substantially higher policy entropy than either SFT initialization, and the separation remains visible through the available trajectories. At the in-domain initialization, OPD also has higher answer diversity and pass@16 ($+2.0$ to $+5.2$ points over SFT), although problem-level bootstrap intervals show that the smaller contrast is uncertain. The advantage is absent after RL (endpoint pass@16 values within $1.1$ points) and on MathVista (six models within $1.2$ points). Our contribution is therefore a bounded empirical characterization: Stage-1 is strongly associated with the entropy regime in this setup, but the downstream payoff is small, localized, and not evidence that OPD is a better RL warm-start.

The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice, when closed-form formula are not available for expressing convex conjugates of given functions, one must approximate them using various techniques. One recent such versatile numerical method is the deep Legendre transform method which relies on neural networks although it remains challenging particularly for tackling ill-conditioned functions. This work builds on the reformulation of the LF transform as a projective polarity. A notable property of this framework is its affine invariance. We leverage this affine invariance to introduce a Hessian-based preconditioning strategy. Specifically, we apply an affine deformation around a minimizer so that the second-order Taylor approximation of the function coincides with the canonical paraboloid, whose conjugation map is the identity. A residual network initialized near the identity can then learn this simplified mapping, while the original conjugation map is recovered through the inverse deformation. The proposed preconditioning incurs only a modest computational overhead, consisting of a single eigendecomposition during initialization and two matrix-vector multiplications per query. Experiments on a diverse set of convex functions, including high-dimensional benchmarks, demonstrate improved convergence rates and enhanced numerical accuracy of the conjugation, with particularly significant gains for ill-conditioned problems. Finally, we discuss the scope of applicability of our proposed method and highlight several of its limitations.

Process Reward Models (PRMs) improve credit assignment for reasoning by providing step-level feedback. However, we identify a hidden bias in PRMs caused by severe imbalance in step-level training data. Standard cross-entropy training amplifies this bias, causing PRMs to overcredit plausible but incorrect steps and produce high false-positive rates. We show that these false positives have an asymmetric downstream effect: false negatives mainly slow exploration, whereas false positives actively steer Best-of-N selection, guided decoding, and policy optimization toward flawed reasoning. This suggests that PRM training should shift from pointwise label fitting to reliable relative comparisons. To address this, we propose PRISM (Precision Ranking for Improved Step Modeling), a policy-aware PRM training framework that learns from contrastive step-level comparisons and hard negatives generated by a temporal lookahead strategy, requiring no new human labels. We further use a difficulty-aware curriculum to optimize the contrastive step margin. Across PRMBench and ProcessBench, PRISM substantially reduces false positives (22% on PRMBench) and improves macro F1 over strong discriminative PRMs. When applied to policy optimization and search tasks, including guided decoding and Best-of-N selection, it consistently improves accuracy (up to 22% for guided decoding and 33% for Best-of-N) and robustness. More broadly, trustworthy process supervision is not just about assigning high rewards, but about rewarding the right reasoning for the right reasons.

On-policy distillation (OPD) has recently emerged as an important post-training paradigm. By using a stronger teacher model to provide dense, fine-grained supervision for sampled trajectories, OPD offers a clear advantage over reinforcement learning with verifiable rewards (RLVR), which typically depends on sparse binary or outcome-based environmental feedback. However, naive token-level distillation can suffer from gradient instability, due to magnitude misalignment in outlier states. To address this issue, we propose Globally Normalized Distillation Policy Optimization (GNDPO), a practical method that stabilizes optimization by transforming raw KL scores into batch-level relative advantages. This normalization effectively mitigates gradient explosions while retaining the benefits of token-level guidance. Experimental results show that GNDPO substantially improves training robustness and downstream performance across multimodal reasoning tasks. The code is released at https://github.com/OPPO-Mente-Lab/GNDPO.

The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks. Nonetheless, conventional GPU-based training remains highly energy-demanding, motivating the exploration of physical dynamics and compatible energy-based learning schemes, such as equilibrium propagation (EP). EP-based training, however, frequently suffers from convergence to local minima due to phase-space contraction. Here we introduce an Ising-dynamics-inspired equilibrium-propagation framework in which dissipative Hopfield relaxation is replaced by an extended phase-space dynamics with conjugate variables. The resulting training paradigm keeps the local two-phase learning rule of EP while changing the physical route by which neural states reach equilibrium. We show that this dynamics lowers effective energy barriers, accelerates convergence, improves noise robustness, and trains deep convolutional Hopfield networks on MNIST, FashionMNIST, and CIFAR-10 with performance comparable to backpropagation.

While Ising machines serve as advanced physical solvers for the Ising model,enabling applications in combinatorial optimization and neural network training,their scalability for large-scale neural networks remains constrained by hardware connectivity limitations and suboptimal training methodologies. In this work,we leverage a Coherent Ising Machine (CIM) to train an energy-based neural network using Equilibrium Propagation, achieving performance comparable to existing software-based implementations. We further enhance the algorithm by integrating the Adam optimizer to solve for the ground state of a Hopfield energy network, significantly improving convergence speed and solution accuracy. Additionally, we demonstrate the scalability of our approach across deeper network architectures and convolutional operations. Our results highlight the potential of CIM dynamics as a scalable platform for training complex neural networks, offering a pathway toward energy-efficient implementations via analog circuits, optoelectronics, or integrated photonics. This work establishes a novel physical framework for next-generation AI hardware development.

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, $\exp(-\mathrm{MSE})$), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by $2.3\times$, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

Spatio-temporal graph neural networks (STGNNs) have become the dominant approach for traffic prediction, yet their computational requirements pose challenges for practical deployment in intelligent transportation systems (ITS). While recent work has proposed efficient alternatives to STGNNs, a fundamental question remains unexplored: are these architectures themselves over-parameterised? We examine this question using the Spatio-Temporal Graph Convolutional Network (STGCN), one of the most widely adopted models in this domain. Through systematic experiments across four diverse traffic datasets, we compare 1-block, 2-block (standard), and 3-block STGCN variants. Our findings reveal that the single-block architecture achieves optimal performance for short-term prediction (10 mins) on three of four datasets, while incurring only marginal degradation ($\leq$1.8% relative error) at longer horizons. Crucially, the 2-block variant incurs 61% higher CPU inference latency and 37% lower throughput relative to 1-block -- substantial overhead for resource-constrained ITS deployment. The 3-block architecture offers no favourable tradeoff, more than doubling computational cost for $<$0.5% relative improvement. These results suggest that the default 2-block STGCN may be over-parameterised for many applications, with implications for both practitioners deploying traffic prediction systems and researchers benchmarking efficiency-focused methods.

Interpretability increasingly treats groups of components, not individual units, as the basic object, and proposes to find them by clustering co-activation statistics. We ask whether such a cheap signal actually identifies an attention-head circuit. Adapting a sparse-autoencoder clustering recipe to attention heads -- but validating by causal ablation rather than reconstruction -- we cluster heads and then run a closure test: ablate the discovered community and compare per-example damage to matched-random controls. Across two dense 1B-scale models (Pythia 1B, OLMo 1B) and two input distributions, the communities pass closure. In a Mixture-of-Experts model (OLMoE-1B-7B), route-conditional clustering recovers a statistically real signal that nonetheless does not survive closure -- ablation improves loss, the wrong direction. Extending closure across training, attention-target selectivity and participation ratio decouple from function in both directions. We conclude that a cheap signal is a circuit proposal, not a confirmed circuit; closure is what separates them.

Muon has recently emerged as a state-of-the-art optimizer for pretraining Large Language Models (LLMs) and vision classifiers. Despite its efficiency advantage over Adam and SGD, the feature-learning advantage of Muon remains unclear. This paper investigates Muon's feature-learning advantage through the lens of robustness and transferability. First, by evaluating pretrained models on corrupted images and texts, we show that features learned by Muon are consistently more robust than those learned by Adam and SGD across different architectures, including transformers and Convolutional Neural Networks (CNNs). Using trained layer-wise probes, we further show that this robustness advantage is reflected in larger logit margins across layers. Second, by training linear classifiers or fine-tuning full models from pretrained parameters on downstream tasks, we demonstrate that Muon-learned features transfer more effectively than those learned by Adam and SGD. This transferability advantage is further supported by the diversity of hidden states across layers, as measured by effective rank. Finally, in a representative classification problem with multi-component features, we prove that Muon attains larger margins and higher effective rank than Adam and SGD, providing theoretical support for our empirical findings.

Responses to perturbations are key to understanding physical systems. The ability to contrast such responses by comparing how a system reacts under slightly different conditions provides a mechanism for learning. Here, we introduce Perturbative Contrastive Physical Learning (PCPL), a general framework in which learning emerges from measurable contrasts between physical states produced by controlled changes to inputs, boundary conditions, parameters, or interpreter functions. PCPL unifies and extends prior approaches: Equilibrium Propagation is rooted in contrasts between free and nudged equilibria in energy-based systems, while Frequency Propagation corresponds to contrasts extracted from sinusoidally driven, frequency-demodulated responses. We show that contrast-driven updates can reflect either local sensitivities or global inverse-problem structure, yet do not require centralized gradient computation. Instead, effective learning geometry emerges implicitly from the system's own physical response, allowing learning behavior to arise without an external processor or explicit backpropagation. We demonstrate PCPL in two platforms: (i) spring networks that update bond stiffness using measured displacements and forces, and (ii) continuous-variable photonic circuits trained via x quadrature measurements and finite-difference estimates of the Jacobian. Both platforms successfully learn classification tasks. We further show that a continuous-variable photonic circuit can be trained to implement analog multiplication, illustrating a step toward more autonomous physical learning systems.

We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yielding models that respect the geometric support of physical quantities and expose conservation and compatibility structure. We further propose Hierarchical TNOs (HTNOs), which incorporate learned coarse complexes to propagate long-range and topology-dependent information. Our framework subsumes existing NOs as a special case, providing a unified perspective on operator learning across discretizations. Across a range of PDE benchmarks, including irregular-geometry flow problems, TNOs and HTNOs improve accuracy; controlled studies further isolate the benefits of native higher-rank and topological structure. Project page: https://circle-group.github.io/research/TNO

Function-vector (FV) heads (Todd et al., 2024) are typically identified by the magnitude of their causal contribution to in-context rule tasks, under the implicit assumption that the top set is a homogeneous functional class. This assumption fails. We replace magnitude-only ranking with a sign-preserving criterion (refined DLA + permutation FDR) and validate each candidate by path patching. The FV head population then splits into two opposing sub-populations: writers push the rule-correct logit up; cancellers push it down. A four-condition canonical verdict holds in $13/15$ cells across three model families and six Pythia scales, and a sign-shuffle rejects homogeneity in $5/6$ main cells. The structure is invisible to magnitude-only ranking: Todd's top-$20$ captures $64\%$ of cancellers but only $4\%$ of writers on the hierarchical task, and $59\%$ of writers but only $8\%$ of cancellers on the modular task. We rule out six artefact accounts on all $27$ canceller (cell, head) pairs: induction overlap, sinks, generic importance, rank-$1$ copy-suppression, V-cascade, and rank-nearest non-FV controls. Zero-ablating cancellers yields $+0.13$ to $+0.29$ nats of logit gain in $6/6$ main cells with a directionally consistent $+2$ to $+7$ pp accuracy effect.

Large vision language models (LVLMs) have made rapid advancements and are deployed across various applications, yet hallucinations remain a major challenge. Activation steering is appealing due to its minimal training overhead and controllability at inference time. However, we found that during autoregressive decoding, visual conditioning affects token prediction sparsely and locally across decoding steps, and many existing methods that average image-versus-no-image differences over the entire sequence dilute these critical signals, yielding low signal-to-noise ratio steering directions. Additionally, many existing methods apply a fixed steering strength, which misallocates the intervention budget, over-perturbs non-critical tokens, and can cause instability. To address these limitations, we propose Token-Level Visual-Sensitivity Steering (TLVS) for hallucination mitigation. Our approach first extracts token-level steering vectors and refines them, and then applies fine-grained, visual-sensitivity-adaptive steering only where it matters. This lightweight, plug-and-play mechanism requires only minimal training for calibration and can be applied across diverse vision-language models. It modulates the steering strength at each decoding step, selectively suppressing hallucination-prone spans while preserving evidence-grounded content. We evaluate TLVS on several benchmarks, including POPE, AMBER, CHAIR (COCO), MMHal, and HallusionBench, demonstrating consistent improvements over previous steering methods.

Traffic sign recognition is crucial for intelligent transportation and autonomous driving, as it can improve driving efficiency and ensure road safety. However, traditional recognition methods are based on large datasets and intensive computation, which limits their real-time applicability. Spiking Neural Networks (SNNs) offer a biologically inspired, energy-efficient alternative due to their spatiotemporal processing capabilities, but suffer from information loss and vanishing gradients during training. To overcome these limitations, this study proposes a Quantum Deep-supervised Spiking Neural Network (QDS-SNN) that integrates Quantum Neural Networks (QNNs) for efficient, low-power deep supervision. Using quantum superposition and entanglement, QNNs enable expressive representations and parallel computation, thereby enhancing performance without compromising energy efficiency. The proposed QDS-SNN incorporates a temporally and spatially adaptive LIF (TSA-LIF) neuron and a quantum-assisted classifier module (QACM) to mitigate gradient issues and improve training effectiveness. This study conducts experiments on the PennyLane quantum simulation platform, and the results show that QDS-SNN achieves 99.72\% accuracy on the GTSRB dataset in only 6 time steps -- outperforming the MS-ResNet baseline by 1.32\% while reducing energy consumption by 55.77\%. In the TSRD dataset, it achieves 97.90\% accuracy while reducing energy use to 52.68\% of the baseline. These results demonstrate that QDS-SNN offers a high-performance, energy-efficient solution for traffic sign recognition in intelligent transportation systems.

Smartphone telephoto cameras are approaching a "telephoto physics wall": as pixel pitches shrink toward sub-0.5 micron, the optics remain limited by geometric aberrations, leading to diminishing returns on resolution. Traditional Image Signal Processors (ISPs) cannot eliminate these aberrations, because they operate through local, stage-wise processing with no explicit model of the underlying point spread function (PSF). We demonstrate how a learning-based Neural ISP for image restoration, trained on the underlying degradations, inverts what stage-wise pipelines cannot, turning small-pixel designs into a net advantage. We investigate this through a controlled simulation of a representative telephoto module, evaluating five configurations (0.35--0.75 micron pixel pitch). The aperture is scaled proportionally to keep per-pixel SNR and diffraction spot size fixed, thereby isolating geometric aberration and spatial sampling. While the traditional ISP improves only modestly with smaller pixels, the Neural ISP scales substantially: at 0.35 micron} it reaches 745 cycles/mm MTF50 (vertical), a 2.5--3x resolution improvement over the traditional ISP, and LPIPS improves significantly from 0.244 to 0.151 while traditional results stay comparatively flat. In a low-SNR extension (15 dB per-frame bursts at 0.35 micron), a multi-frame Neural ISP recovers performance close to the bright-light single-frame baseline, whereas a multi-frame traditional ISP shows no meaningful improvement -- indicating that traditional pipelines at small pixels are bottlenecked by uncorrected PSF blur rather than by noise. These results point to a design philosophy in which Neural ISPs enable high-resolution telephoto modules by correcting residual optical aberrations rather than requiring increasingly complex optics.

Large language models (LLMs) have demonstrated remarkable reasoning abilities on mathematical and multi-hop planning tasks. The CoCoNuT (Chain of Continuous Thought) paradigm~\cite{hao2024coconut} extends this by enabling models to reason in latent space, exploring multiple reasoning paths simultaneously rather than committing to a single chain early on. However, we identify a limitation we term the \textbf{concept bottleneck}. At each reasoning pass, intermediate hidden states are overwritten, causing the model to lose critical facts computed in earlier steps as reasoning depth increases. We observe this empirically. On HotpotQA, vanilla CoCoNuT (10.4\% EM) fails to improve over the CoT baseline (11.0\% EM), and performance degrades with curriculum depth on GSM8K. To address this, we propose \textbf{AGCLR} (Adaptive Gated Continuous Latent Reasoning), which augments CoCoNuT with a \textit{Gated Concept Stream}. A persistent residual memory maintained across all reasoning passes, controlled by three learned gates: a \textit{write} gate that commits intermediate facts to memory, a \textit{read} gate that retrieves relevant prior states, and a \textit{forget} gate that prunes irrelevant context. Evaluated on GSM8K, HotpotQA, and ProsQA using GPT-2 as our base model, AGCLR achieves consistent improvements across all types of datasets. With the performance gap compounding as curriculum depth increases, directly resolving the concept bottleneck. Code available at https://anonymous.4open.science/r/JJJJ/README.md

Vision Transformers operate on fixed patch grids, which can introduce phase-dependent instability for dense prediction: changing the patch partition can change the token evidence available to a pixel, especially near boundaries. We formalize patch-grid phase as a nuisance variable and propose Phase Marginalization, a post-hoc marginalization method that evaluates structured patch-grid phases, inverse-aligns dense outputs, and aggregates them in the original image coordinate system. The central variant, Uniform Phase Marginalization with K = 4, is training-free and improves over the canonical K = 1 baseline across measured segmentation, depth, and local matching settings. In a controlled Cityscapes experiment, Uniform Phase Marginalization provides a modest compute-matched advantage over generic shift-based four-forward test-time augmentation (TTA) (+0.31 mean Intersection-over-Union over the strongest tested generic row). A scaling study further shows that K = 4 is a practical cost-accuracy trade-off: K = 8 is essentially unchanged and K = 16 adds little accuracy at much higher latency. These results position patch-grid phase as a measurable nuisance variable and Phase Marginalization as a simple diagnostic and post-hoc marginalization baseline for dense ViT prediction.

Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Standard transformers apply self-attention uniformly at every layer and token, regardless of whether the input requires dynamic cross-token interaction. We propose CHIAR-Former (Chiaroscuro Attention), a 4-layer hybrid transformer that routes each token to one of three operators - DCT spectral mixing, RBF kernel mixing, or full self-attention - based on per-token spectral entropy, a theoretically justified complexity signal. Through systematic ablation on WikiText-103, we discover routing collapse: the router consistently rejects RBF in favour of DCT and attention, revealing that spectral mixing and dynamic attention are complementary and sufficient. A purpose-designed DCT+Attention-only variant achieves Val PPL 36.54 on WikiText-103 - a 45% improvement over a full-attention baseline (PPL 66.62) at 62.5% fewer attention FLOPs. We extend evaluation to WikiText-2, IMDB sentiment classification, and synthetic ListOps operations, establishing a clear operating regime: CHIAR-Former excels on large-scale naturalistic text where token diversity supports spectral specialisation, while full attention retains an edge on small datasets and synthetic pattern-matching tasks. These findings - both the wins and the losses - together define when and why spectral routing earns its keep.

Modern language models represent text using discrete token-level embeddings, which forces recurring multi-token patterns to be learned implicitly across Transformer layers. Both Over-tokenized Transformers and Engram attempt to address this limitation by explicitly incorporating multi-token (n-gram) memories. However, they rely on separate hash tables for each n-gram order, which introduces hash collisions and prevents nested n-grams from sharing the underlying latent structures. To address these issues, we propose Tensorized Engram (TN-gram), a compact memory module that represents tensorized n-gram embeddings through shared factors in the Canonical Polyadic (CP) form. TN-gram learns shared token-position factors together with order-absorption vectors to encode the embeddings of different n-gram order. Comprehensive experiments demonstrate that TN-gram matches or even outperforms Engram-style n-gram modules while requiring much fewer parameters.

We recast predictive coding as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. We study first a single-level problem and then a multi-level hierarchy. For the single-level problem, we show that proximal gradient descent is precisely a leaky firing-rate network: the membrane leak, the effective recurrent matrix, the local synaptic drive, and the static nonlinearity all follow from one optimization principle, and the resulting circuit is the one proposed by Rao and Ballard. The prior selects the nonlinearity through its proximal operator, and the likelihood precision sets the gain on the observation. For the hierarchy, we show that a classical variable-splitting relaxation of the deep MAP problem yields hierarchical predictive coding as the interconnection of local and distributed solvers. In probabilistic modeling terms, this relaxation replaces the directed generative chain by an undirected Markov random field whose node potentials are the level-wise priors. Each level then applies its own activation function, namely the proximal operator of its prior.

Action-supervised fine-tuning of vision-language-action (VLA) policies fits demonstrations effectively but constrains only the directions that change predicted actions, leaving visual structure consistent across action-equivalent states free to collapse. We formalize this as residual visual collapse along local action fibers and propose FiberTune, a training-time objective that preserves teacher-structured visual residuals without adding inference-time overhead. FiberTune uses an online action probe to estimate action-predictive feature directions, filters them from intermediate visual-token representations, and aligns the resulting probe-filtered residuals to a frozen visual teacher while regularizing their effective rank. Under identical training conditions, FiberTune improves over task-loss-only fine-tuning in every one of six controlled simulation settings spanning two benchmarks and two architectures (pi_0.5 and OpenVLA-OFT), as well as on physical SO-101 pick-place; representative gains include +10.7 percentage points SR(5) on long-horizon CALVIN ABC-to-D and physical SO-101 task success rising from 72.7% to 78.1%. Residual diagnostics show that these gains coincide with increased probe-filtered residual teacher alignment and effective rank, consistent with the action-fiber motivation.

Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations. Solver learning reduces this cost by adapting scalar coefficients, timesteps, or both, while keeping the backbone model fixed. In this work, we identify a structural bottleneck in this update family: each step remains span-limited. Since the scalar-coefficient update lies in the span of buffered velocity evaluations, it can fit only the in-span component while leaving any out-of-span residual unreachable by scalar recombination alone. We propose SpanLift, a lightweight neural solver that augments scalar-coefficient updates with a spatial residual operator. SpanLift keeps a fixed base solver as an in-span prior and learns a spatial residual operator over the state and velocity buffer. The operator is trained by endpoint teacher matching, preserves the pretrained backbone, and adds no model NFEs. Empirically, the learned correction transfers across base solvers and is predominantly out-of-span. Across pixel-space diffusion, latent flow matching, and precipitation nowcasting, SpanLift achieves state-of-the-art few-step sampling. With only 3 NFE, it improves CIFAR-10 FID from 8.16 to 5.69 and ImageNet FID from 17.37 to 11.83.

Linear attention reformulates sequence modeling as recurrent state evolution, enabling efficient linear-time inference. Under the key-value associative paradigm, existing approaches restrict the role of the query to the readout operation, decoupling it from state evolution. We show that query-conditioned state readout induces a structured value prediction over accumulated memory that complements key-based retrieval. Based on this insight, we propose Q-Delta, a query-aware delta rule that integrates mixed key-query prediction errors into state evolution, enabling jointly corrective dynamics while preserving delta-rule efficiency. We establish stability guarantees for the resulting dynamics and derive a hardware-efficient chunkwise-parallel formulation with a custom Triton implementation. Empirical results demonstrate stable optimization, competitive throughput, and consistent improvements over strong baselines on language modeling and long-context retrieval tasks.

Mixture-of-Experts (MoE) scales model capacity efficiently by selectively routing inputs to a specialized subset of experts. However, input-expert specialization, the core motivation of MoE, critically depends on whether the router is actually aware of input structure. In practice, MoE routing is typically implemented as a shallow linear projection with limited awareness of input representation, which often leads to unstable routing. We propose STAR, a Structure Aware Routing that rethinks MoE routing as a subspace learning problem by augmenting standard learnable routing with an evolving principal subspace that tracks dominant input structure via Generalized Hebbian Algorithm (GHA). By aligning routing decisions directly with input structure, STAR enables stable expert specialization. We evaluate STAR on controlled synthetic setup and large-scale language and vision tasks, where it consistently improves routing quality and downstream performance over strong MoE baselines. Moreover, optional test-time subspace updates further enhance routing robustness and generalization under input distribution shifts.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for eliciting long-chain reasoning in large language models. However, existing methods based on Group Relative Policy Optimization (GRPO) rely on a binary outcome reward, which induces two structural failure modes: Zero-Advantage Collapse, in which all rollouts in a group share the same outcome and the gradient vanishes, and Hallucinated Certainty, in which the model becomes increasingly confident on incorrect rollouts late in training. We address both modes by densifying the reward with intrinsic signals computed entirely from the policy's own conditional probabilities, and propose ISPO (Intrinsic Signal Policy Optimization, which combines a sequence-level signal measuring how informative the thinking trajectory is for the final answer, with a token-level directional reward whose hallucinated-certainty hinge penalizes confidently-wrong predictions at critical decision tokens. Across three base models and five mathematical reasoning benchmarks, ISPO consistently outperforms competitive baselines, with the largest gains on the hardest benchmarks where zero-advantage collapse is most frequent, and training-dynamics diagnostics confirm that both failure modes are decreased.

The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces. Its efficient implementation is based on the multi-dimensional Fourier transform. By deriving general regularity bounds for the FNO with respect to both the spatial and parametric variables, we prove that the generalization error of the FNO can be improved by replacing spatial tensor product grids with purpose-built rank-1 lattice points, and by using a second lattice carefully constructed as training points in the parametric space. We achieve more accurate and efficient approximations from fewer network parameters, fewer spatial points, and fewer training samples. In addition, the architecture is simplified, because the high-dimensional Fourier transform on rank-1 lattices requires only a \emph{one-dimensional fast Fourier transform}, and we can use a \emph{hyperbolic cross} frequency index set with lattice points. We demonstrate the benefits of our \emph{lattice-based hyperbolic-cross FNOs} for an elliptic PDE on the torus.

A classical universal stabilization formula offers the practitioner no design freedom: it is a single, parameter-free object. We introduce a cost-parametrized family of stabilizing feedback laws, where (1) the user chooses a function that serves as the running cost on control in an inverse-optimal cost functional, and (2) obtains, through a formula, a nonlinear "expander" of a pre-existing universal controller, which solves an infinite-horizon optimal control problem with a meaningful cost on the state. The cost-to-expander formula is a three-step construction, involving, inter alia, cost differentiation and function inversion-overall, a nonlinear infinite-dimensional operator. The cost-to-expander operator is proven Lipschitz, which enables uniform neural operator approximation of the entire family and supports both offline performance exploration and online adaptation. Semiglobal practical asymptotic stability and second-order suboptimality bounds are established under the approximation. The operator learning and its use in semiglobal stabilization are illustrated numerically. We call the result 'half-direct-optimal' because the paper's design is less than a general 'direct optimal' (HJB-inducing) control, but more than the fully inverse optimal, since the user performs minimization for an arbitrary given cost on control. The dual to the half-direct problem we solve is the problem in which the cost on the state is arbitrary and given. This dual problem is easier and outside of the scope of the paper.

Multimodal large language models (MLLMs) commonly inherit the deep, symmetric Transformer backbone designed for unimodal text modeling, and apply the same computation uniformly to image and language tokens. This design overlooks a key modality asymmetry: image and text tokens differ substantially in information density, redundancy, and required reasoning depth. Through a layer-wise analysis of LLaVA-1.5, we observe that vision tokens tend to saturate in the middle layers. Specifically, text-to-image attention decreases from 0.68 at layer 0 to 0.07 by layer 4, and stabilizes near 0.04 after layer 18, whereas text tokens continue to benefit from deep semantic processing. These findings suggest a mismatch between architectural symmetry and depth-asynchronous modality evolution, resulting in redundant visual computation and possible drift in perceptual representations during deep task-specific adaptation. Motivated by this, we propose Dual-Path Vision Token Routing (DPVR), a modality-asymmetric routing framework for efficient MLLMs. Its core instantiation, DPVR-LF (Late-Layer Fusion), routes vision tokens at the saturation point into a one-layer trainable side branch, runs a thirteen-layer text-only forward that skips image positions in the deep stack, and re-fuses the visual and textual streams only at the final layer. With approximately 3% trainable parameters, DPVR-LF preserves competitive multimodal performance on standard benchmarks while reducing visual computation in the deep Transformer stack. The results challenge the conventional assumption that vision tokens must traverse all deep language-model layers, and indicate that a single late fusion layer can be sufficient for maintaining strong perceptual competence in LLaVA-style MLLMs.

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

Supervised fine-tuning (SFT) is an efficient approach for downstream task adaptation and often serves as the initialization stage for reinforcement learning (RL), but it can show weaker generalization than RL. A key limitation is its off-policy objective: SFT fits fixed demonstrations token by token, including targets poorly aligned with the model's pretrained distribution, which can lead to overfitting. A recent line of work addresses this issue by assigning larger training weights to tokens better aligned with the current model's predictive distribution, with the intuition that fitting these tokens are less distortive to the model's pretrained knowledge and representations. However, computing the token weights from the model that is currently fine-tuned entangles token weights with the optimization trajectory, inducing a self-reinforcing dynamics as the distribution rapidly departs from the pretrained model. To address this, we propose PriFT (Prior-support guided Fine-Tuning), which derives token weights from a frozen pretrained reference to obtain a stable reweighting signal unaffected by fine-tuning. This signal estimates prior support: the extent to which each target token is supported by the pretrained distribution. Across multiple existing token-reweighting rules, replacing the reweighting signal from the online model to pretrained model consistently improves performance. We introduce two instantiations: PriFT-prob uses pretrained token probability, while PriFT-mass selects tokens by cumulative probability mass under the pretrained distribution. Extensive experiments on mathematical reasoning, code generation, and medical question answering show that PriFT achieves state-of-the-art results among SFT baselines and provides a better initialization for subsequent RL training.

Training parameterised quantum circuits (PQCs) on quantum hardware is bottlenecked by the measurement cost of gradient estimation, which under the parameter-shift rule scales linearly in the number of trainable parameters and dominates the total shot budget of training at scale. In this work, we propose a framework of forward gradient estimators for PQCs, based on the forward mode of automatic differentiation, that yields an unbiased estimator of the gradient by averaging a freely tunable number of random directional derivatives and recovers SPSA, random coordinate descent, and the parameter-shift rule as limiting cases, with no ancilla qubits or controlled-gate overhead. We prove that stochastic quantum forward gradient descent converges under standard assumptions, with an explicit second-moment expansion that interpolates between the single-direction extreme of SPSA and the full-gradient extreme of parameter-shift. Within this framework we derive QUIVER (Quantum Iterative V-adaptive Estimator Rule), an adaptive optimiser for parameterised circuits whose update rule follows from a closed-form minimum measurement-cost allocation. We show numerically that forward gradients train Hamming-weight-preserving orthogonal quantum neural networks with up to 60 qubits and 1770 parameters on the ECG5000 and MNIST datasets orders of magnitude more efficiently than the parameter-shift rule. We also demonstrate that our proposed QUIVER optimiser can outperform iCANS and gCANS measurement-frugal optimisers on optimisation problems using the quantum approximate optimisation algorithm and quantum simulation with the variational quantum eigensolver.

We present \textbf{Echo-Memory}, a controlled study of memory mechanisms in action-conditioned world models. These models generate multi-segment videos from a first frame, text prompt, and camera-action sequence, but their central failure is often memory rather than local image synthesis: after the camera leaves and returns, the scene or salient object may silently change. Existing memory designs are hard to compare because gains are entangled with backbone, training, retrieval, and evaluation differences. Echo-Memory fixes the action-to-video interface and varies only how history is stored and read by the generator. Under a shared video diffusion backbone, optimizer, camera-action representation, sampler, and evaluation pipeline, we compare raw context, compression-based memory, spatial summaries with different read-out paths, and state-space recurrence. This matched matrix separates four otherwise conflated axes: \emph{capacity}, \emph{compression}, \emph{read-out}, and \emph{recurrence}. We also evaluate memory through a three-branch protocol: replay quality, in-domain loop revisit, and open-domain return probes. The branches routinely disagree, showing that replay fidelity is not a sufficient proxy for remembering a world. Three findings follow. Raw context is a strong capacity baseline and improves open-domain return far more than it improves replay metrics. Compactness is not a free substitute for capacity: aggressive spatial and hybrid-compression memories lose the salient evidence needed for return. Finally, block-wise state-space recurrence is the strongest open-domain return mechanism in our matrix, showing that the structure of implicit memory matters as much as the decision to use it. These results provide a compact protocol for studying memory in action world models beyond isolated replay metrics.

It is becoming increasingly common in regression to train neural networks that model the entire distribution even if only the mean is required for prediction. This additional modeling often comes with performance gain and the reasons behind the improvement are not fully known. This paper investigates a recent approach to regression, the Histogram Loss, which involves learning the conditional distribution of the target variable by minimizing the cross-entropy between a target distribution and a flexible histogram prediction. We design theoretical and empirical analyses to determine why and when this performance gain appears, and how different components of the loss contribute to it. Our results suggest that the benefits of learning distributions in this setup come from improvements in optimization rather than modelling extra information. We then demonstrate the viability of the Histogram Loss in common deep learning applications without a need for costly hyperparameter tuning.

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire minimization process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer biologically plausible, ePC numerically computes exact PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures on digital hardware and beyond.

The attention mechanism in a Transformer architecture matches key to query based on both content -- the what -- and position in a sequence -- the where. We present an analysis indicating that what and where are entangled in the popular RoPE rotary position embedding. This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call Polar Coordinate Position Embeddings or PoPE, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities compared not only to RoPE but even a method designed for extrapolation, YaRN, which requires additional fine tuning and frequency interpolation.

We introduce the Similarity-Distance-Magnitude (SDM) activation function, a more robust and interpretable formulation of the standard softmax activation function, adding Similarity (i.e., correctly predicted depth-matches into training) awareness and Distance-to-training-distribution awareness to the existing output Magnitude (i.e., decision-boundary) awareness, and enabling interpretability-by-exemplar via dense matching. We further introduce the SDM estimator, based on a data-driven partitioning of the class-wise empirical CDFs via the SDM activation, to control the class- and prediction-conditional accuracy among selective classifications. When used as the final-layer activation over pre-trained language models for selective classification, the SDM estimator is more robust to covariate shifts and out-of-distribution inputs than existing calibration methods using softmax activations, while remaining informative over in-distribution data.

Scientific data acquisition continues to outpace storage and analysis capabilities, making voxel-based representations increasingly intractable. Implicit neural representations (INRs) offer a promising solution by encoding signals through coordinate-based neural networks, serving as surrogates of data, with computational and storage requirements scaling with network complexity rather than data dimensionality. However, smaller INRs struggle to faithfully represent the multi-scale structures, high-frequency information, and fine textures that constitute a large proportion of scientific measurements. We propose WIEN-INR, a theoretically-guided hierarchical INR framework that distributes modeling across resolution scales and enables improved representation capacity through a novel enhancement network to recover subtle details. This multi-scale architecture allows smaller networks to retain the full spectrum of information while preserving training efficiency and lowering storage cost. Evaluated on distinct raw experimental measurements across scales and complexities, WIEN-INR represents a practical step toward broader adoption of neural representations in scientific workflows, delivering compact, robust, and high-fidelity representations.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a novel two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky\_ReLU, ELU, SELU) using a differentiable hard mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of different architectures. Our analysis reveals that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures. We also demonstrated that SmartMixed effectively trains the network by allowing neurons to select their preferred activation functions, competing against models using a single fixed state-of-the-art activation function.

Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing equations, often producing overly complex or inaccurate expressions. To address this, we present a decomposable SR method that generates interpretable multivariate expressions leveraging transformer models, genetic algorithms (GAs), and genetic programming (GP). In particular, our explainable SR method distills a trained ``opaque'' regression model into mathematical expressions that serve as explanations of its computed function. Our method employs a Multi-Set Transformer to generate multiple univariate symbolic skeletons that characterize how each variable influences the opaque model's response. We then evaluate the generated skeletons' performance using a GA-based approach to select a subset of high-quality candidates before incrementally merging them via a GP-based cascade procedure that preserves their original skeleton structure. The final multivariate skeletons undergo coefficient optimization via a GA. We evaluated our method on problems with controlled and varying degrees of noise, demonstrating lower or comparable interpolation and extrapolation errors compared to two GP-based methods, three neural SR methods, and a hybrid approach. Unlike them, our approach consistently learned expressions that matched the original mathematical structure. Similarly, our method achieved both a high symbolic solution recovery rate and competitive predictive performance relative to benchmark methods on the Feynman dataset.

Controlling autonomous systems under real-world conditions often requires policies that can be evaluated with low latency and minimal energy consumption. Unfortunately, these conditions are at odds with the use of high-precision deep neural networks as controllers. In this work, we introduce Differentiable Weightless Controllers (DWCs), a symbolic-differentiable architecture that learns flexible, non-linear, yet highly efficient control policies. DWCs can be trained end-to-end via gradient-based techniques, yet compile directly into FPGA-compatible circuits with few- or even single-clock-cycle latency and nanojoule-level energy cost per action. Across five MuJoCo benchmarks, including high-dimensional Humanoid, DWCs achieve returns competitive with standard deep policies (full-precision or quantized neural networks). Furthermore, DWCs exhibit structurally sparse and interpretable connectivity patterns, enabling direct inspection of which input values influence control decisions.

We introduce Lattice, a hybrid sequential prediction system that conditionally activates learned behavioral structure using binary confidence gating. The system summarizes behavior windows as behavioral archetypes and activates archetype-based scoring only when an in-support confidence signal exceeds a validation-calibrated threshold, falling back to backbone predictions when uncertain. Our primary estimand is the controlled effect of adding Lattice to a fixed backbone on identical test rows. On MovieLens (30 paired seeds, full-catalog ranking), LSTM+Lattice improves HR@10 by +31.7% (gated) versus the LSTM backbone alone (p much less than 10^-20); ungated fusion reaches +58.7% on the same protocol. We do not claim gating maximizes pooled accuracy. With backbone-native archetypes (fit in each backbone's embedding space), gated lifts of +13.3% (transformer) and +17.0% (SASRec) hold under the same evaluation design. A prior approximately 0% transformer row in version 1 reflected an invalid cross-backbone transfer, not evidence that composition cannot help stronger encoders. Amazon Electronics provides supporting cross-domain evidence (+124.0% gated, 15 seeds, high variance). Controlled shift checks (appendix) illustrate gate refusal under distribution shift. Standalone SASRec and BERT4Rec scores are contextual references, not the target estimand. We report what composition achieves and when it activates; production calibration and implementation details remain proprietary pending patent prosecution.

Self-play post-training methods has emerged as an effective approach for finetuning large language models and turn the weak language model into strong language model without preference data. However, the theoretical foundations for self-play finetuning remain underexplored. In this work, we tackle this by connecting self-play finetuning with adversarial imitation learning by formulating finetuning procedure as a min-max game between the model and a regularized implicit reward player parameterized by the model itself. This perspective unifies self-play imitation and general preference alignment within a common framework. Under this formulation, we present a game-theoretic analysis showing that the self-play finetuning will converge to it's equilibrium. Guided by this theoretical formulation, we propose a new self-play imitation finetuning algorithm based on the $χ^2$-divergence variational objective with bounded rewards and improved stability. Experiments on various of language model finetuning tasks demonstrate consistent improvements over existing self-play methods and validate our theoretical insights.

The superficial alignment hypothesis (SAH) posits that large language models learn most of their knowledge during pre-training, and that post-training merely surfaces this knowledge. The SAH, however, lacks a precise definition, which has led to (i) different and seemingly orthogonal arguments supporting it, and (ii) important critiques to it. We propose a new metric called task complexity: the length of the shortest program that achieves a target performance on a task. In this framework, the SAH simply claims that pre-trained models drastically reduce the complexity of achieving high performance on many tasks. Our definition unifies prior arguments supporting the SAH, interpreting them as different strategies to find such short programs. Experimentally, we estimate the task complexity of mathematical reasoning, machine translation, and instruction following; we then show that these complexities can be remarkably low when conditioned on a pre-trained model. Further, we find that pre-training enables access to strong performances on our tasks, but it can require programs of gigabytes of length to access them. Post-training, on the other hand, collapses the complexity of reaching this same performance by several orders of magnitude. Overall, our results highlight that task adaptation often requires surprisingly little information -- often just a few kilobytes.

Time series data are prone to noise in various domains, and training samples may contain low-predictability patterns that deviate from the normal data distribution, leading to training instability or convergence to poor local minima. Therefore, mitigating the adverse effects of low-predictability samples is crucial for time series analysis tasks such as time series forecasting (TSF) and time series classification (TSC). While many deep learning models have achieved promising performance, few consider how to identify and penalize low-predictability samples to improve model performance from the training perspective. To fill this gap, we propose a general Amortized Predictability-aware Training Framework (APTF) for both TSF and TSC. APTF introduces two key designs that enable the model to focus on high-predictability samples while still learning appropriately from low-predictability ones: (i) a Hierarchical Predictability-aware Loss (HPL) that dynamically identifies low-predictability samples and progressively expands their loss penalty as training evolves, and (ii) an amortization model that mitigates predictability estimation errors caused by model bias, further enhancing HPL's effectiveness. The code is available at https://github.com/Meteor-Stars/APTF.

We derive integral formulas that simplify the Vector Signal Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to anti-symmetric couplings. In particular, we obtain explicit closed-form expressions for the anti-symmetric analogues of the Gaunt coefficients. This enables us to simulate the Clebsch-Gordan tensor product using a single Vector Signal Tensor Product, yielding up to a $9\times$ reduction in the required tensor product evaluations. Our results enable efficient and practical implementations of the Vector Signal Tensor Product, paving the way for applications of this generalization of Gaunt Tensor Products in $\mathrm{SO}(3)$-equivariant neural networks. Moreover, we discuss how the Gaunt and the Vector Signal Tensor Products allow to control the expressivity-runtime tradeoff associated with the usual Clebsch-Gordan Tensor Products. Finally, we investigate low rank decompositions of the normalizations of the considered tensor products in view of their use in equivariant neural networks.

Recent vision backbones, such as Transformer families and state-space models like Mamba, have achieved remarkable progress on image recognition. Despite their empirical success, these architectures remain far from the computational principles of the human brain, often demanding enormous amounts of training data while offering limited interpretability. We propose the Vision Hopfield Memory Network (V-HMN), a brain-inspired vision backbone that integrates hierarchical memory mechanisms across layers with iterative refinement updates. Specifically, V-HMN incorporates local Hopfield modules that provide associative memory dynamics at the image patch level, global Hopfield modules that function as episodic memory for contextual modulation, and a predictive-coding-inspired refinement rule for iterative error correction. By organizing these memory-based modules hierarchically, V-HMN captures both local and global dynamics in a unified framework. Memory retrieval exposes the relationship between inputs and stored patterns, providing a prototype-based form of interpretability through explicit memory retrieval, while the reuse of stored patterns improves data efficiency. This brain-inspired design therefore enhances data efficiency and provides a prototype-based form of interpretability compared to existing self-attention- or state-space-based approaches. We conducted extensive experiments on public image classification benchmarks. V-HMN achieves strong performance on small- and medium-scale benchmarks, and remains competitive with widely adopted backbone architectures on ImageNet despite minimal architectural tuning, while offering improved data efficiency and a prototype-based form of interpretability. These findings highlight the potential of V-HMN as a memory-centric alternative to standard vision backbones, thereby bridging brain-inspired computation with modern machine learning.

Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization. However, the orthogonalization quality of Muon hinges on the number of Newton--Schulz (NS) iterations performed, which poses efficiency challenges due to its non-trivial computation and communication cost. We propose Muon$^2$, an extension of Muon, to improve both quality and efficiency by applying Adam-style adaptive second-moment preconditioning before orthogonalization. Our key insight is that the core challenge of polar approximation in Muon lies in the ill-conditioned momentum matrix, of which the spectrum is substantially improved by Muon$^2$, leading to faster convergence toward a practically sufficient orthogonalization. We further characterize the practical orthogonalization quality via directional alignment, under which Muon$^2$ demonstrates dramatic improvement over Muon at each polar step. Across GPT, LLaMA, and Mixture-of-Experts pre-training experiments up to 13B parameters, Muon$^2$ (and its memory-efficient variant Muon$^2$-F that preserves most of its benefits) consistently outperforms Muon and its variants while reducing NS iterations by 40%, and saves up to 1/4 training time over Muon when achieving the same loss.

We introduce MinMax Recurrent Neural Cascades (MinMax RNCs), a class of recurrent neural networks built from a novel form of recurrence over the MinMax algebra. We show that MinMax RNCs enjoy key properties that are difficult to obtain simultaneously: strong formal expressivity, efficient evaluation, stable dynamics, and non-vanishing state gradients. First, their formal expressivity corresponds to the regular languages, arguably the maximal expressivity for finite-memory systems. Second, in addition to evaluation in recurrent form, they also admit parallel-scan evaluation with logarithmic depth and linear work in the input length. Third, their states and activations are uniformly bounded for all sequence lengths. Fourth, their loss gradients exist almost everywhere and are uniformly bounded for all sequence lengths. Fifth, they do not exhibit vanishing state gradients: the gradient of a state with respect to a past state can retain norm one independently of the temporal distance between the states. Empirically, we find that these theoretical properties translate into strong practical performance. MinMax RNCs solve the considered synthetic tasks perfectly, generalise to long sequences, and outperform the recurrent baselines considered in our experiments. We also train a 112M-parameter MinMax RNC for next-token prediction, obtaining competitive performance for its size and providing initial evidence that MinMax recurrence can scale to real-world sequence-modelling tasks.

Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for performance. The Bistable Memory Recurrent Unit (BMRU) was introduced to enable hardware-software co-design of ultra-low power RNNs: quantized states with hysteresis provide persistent memory while mapping directly to analog primitives. However, BMRU performance lags behind parallelizable RNNs on complex sequential tasks. In this paper, we identify gradient blocking during state updates as a key limitation and propose a cumulative update formulation that restores gradient flow while preserving persistent memory, creating skip-connections through time. This leads to the Cumulative Memory Recurrent Unit (CMRU) and its relaxed variant, the $α$CMRU. Experiments show that the cumulative formulation dramatically improves convergence stability and reduces initialization sensitivity. The CMRU and $α$CMRU match or outperform Linear Recurrent Units (LRUs) and minimal Gated Recurrent Units (minGRUs) across diverse benchmarks at small model sizes, with particular advantages on tasks requiring discrete long-range retention, while the CMRU retains quantized states, persistent memory, and noise-resilient dynamics essential for analog implementation.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

Transformers consuming multi-channel scalar signals must embed $C$ simultaneous values into one $d_{\text{model}}$-dimensional vector per time step. We audit eight input encoders -- a shared-scalar baseline, per-channel linear projections, an orthogonality regulariser, a nonlinear MLP, block-partitioned concatenation, channel-independent and channel-as-token architectures, and a projected positional encoding -- on a synthetic benchmark where channel identity is informative and on ETTh1, scored by next-step negative log-likelihood. The headline is practical near-equivalence within a wide "top tier": the standard per-channel linear projection matches every alternative up to small, statistically real but practically modest differences. A direct geometric probe attributes this to a spontaneous orthogonalisation of the per-channel projections: they end up near-orthogonal with no explicit regulariser, letting the standard linear recover channel identity from the summed embedding. Two encoders lose decisively: the shared-scalar baseline collapses for information-theoretic reasons we make explicit, and the channel-independent PatchTST-spirit baseline overfits universally on the synthetic benchmark and underperforms on both. Paired tests resolve two small gaps: projecting the sinusoidal positional encoding through a learned linear layer edges the rest at small $C$ by extending this orthogonality to the positional subspace; a nonlinear MLP stem edges them at the largest $C$, with the gap shrinking under more training data. The practical recommendation: use the standard per-channel linear projection by default; reach for something more elaborate only when the task calls for it.

A central question in vector- and function-valued learning is how to design kernels that capture both local and non-local interactions while remaining computationally tractable. Existing operator-valued kernels offer only partial answers: separable kernels are efficient but fail to model interactions across the function domain, while commutative kernels capture only pointwise structure. To address this, we propose spectral truncation kernels, a new class of positive definite kernels for vector- and function-valued learning based on spectral truncation and $C^*$-algebra. By allowing noncommutative products in the kernel construction, the proposed kernels induce interactions across the data function domain and fill the gap between existing separable and commutative kernels. In addition, by using the $C^*$-algebraic framework, we reduce the computational cost compared to the existing vector-valued RKHS framework with operator-valued kernels.

The reasoning pattern of Large language models (LLMs) remains opaque, and reinforcement learning (RL) typically applies uniform credit across an entire generation, blurring the distinction between pivotal and routine steps. This work positions attention as a privileged substrate that renders the internal logic of LLMs legible, not merely as a byproduct of computation, but as a mechanistic blueprint of reasoning itself. We first distinguish attention heads between locally and globally focused information processing and reveal that locally focused heads produce a sawtooth pattern near the diagonal indicating phrasal chunks, while globally focused heads expose tokens that exert broad downstream influence over future tokens. We formalize these with two metrics: 1) Windowed Average Attention Distance, which measures the extent of backward attention within a clipped window; 2) Future Attention Influence, which quantifies a token's global importance as the average attention it receives from subsequent tokens. Taken together, these signals reveal a recurring preplan-and-anchor mechanism, where the model first performs a long-range contextual reference to generate an introductory token, which is immediately followed by or coincides with a semantic anchor token that organizes subsequent reasoning. Leveraging these insights, we introduce three novel RL strategies that dynamically perform targeted credit assignment to critical nodes (preplan tokens, anchor tokens, and their temporal coupling) and show consistent performance gains across various reasoning tasks. By aligning optimization with the model's intrinsic reasoning rhythm, we aim to transform opaque optimization into an actionable structure-aware process, hoping to offer a potential step toward more transparent and effective optimization of LLM reasoning.

Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential. However, in this paper, we find that for general reasoning tasks (e.g., mathematics and coding), arbitrary order generation may in fact limit the reasoning potential of dLLMs. We observe that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, which can lead to a premature collapse of solution coverage. This observation motivates a rethink of RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We show that effective reasoning can be elicited by simply forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, JustGRPO, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs. Project page: https://nzl-thu.github.io/the-flexibility-trap

Hybrid language models combine softmax attention with linear-time sequence mechanisms such as state-space or linear-attention layers, but the functional contribution of each component type remains insufficiently characterized. We study component-level ablation in two sub-1B hybrid language models, Qwen3.5-0.8B and Falcon-H1-0.5B, using likelihood-based evaluation, downstream benchmarks, layer-wise interventions, random controls, and representation-level diagnostics. Across the tested models, removing either attention or the alternative sequence-processing pathway substantially degrades performance, indicating that both component types contribute to model behavior. Likelihood metrics are especially sensitive to the linear-attention or state-space pathway, while downstream benchmark degradation depends on task and architecture. Layer-wise ablations show that component importance is position-dependent, with the strongest effects concentrated in early or mid-network components rather than uniformly across depth. Random-removal controls further show that hybrid architectures and same-family Transformer baselines degrade differently under structural perturbation. These results suggest that component ablation is a useful diagnostic for understanding hybrid language model architectures. The findings provide evidence relevant to efficient model design, compression, robustness analysis, and deployment decisions in architectures that combine attention with alternative sequence-processing mechanisms.

We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is explicitly taken into account through a higher-order variational formulation that enforces linear growth along the gradient direction away from this discontinuity set. The eikonal equation and the zero-level set of the SDF are enforced as constraints. To make this variational problem computationally tractable, a phase field approximation of Ambrosio-Tortorelli type is employed. The associated phase field function implicitly describes the medial axis. The method is implemented for surfaces represented by unoriented point clouds using neural network approximations of both the SDF and the phase field. Experiments demonstrate the method's accuracy both in the near field and globally. Quantitative and qualitative comparisons with other approaches show the advantages of the proposed method.

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose \textbf{LoPT}: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT

Variational Quantum Algorithms (VQAs) are a leading approach to exploiting near-term quantum hardware, leveraging parameterized quantum circuits and classical optimization to achieve advantage. Despite their promise, the practical deployment of VQAs is challenged by the difficulty of designing quantum circuit architectures that balance expressivity, trainability, and hardware constraints. Existing evolutionary-based quantum neural architecture search methods address these challenges but suffer from high computational costs due to repeated training of candidate circuits. In this work, we identify a setting in which the Gram matrix of the Quantum Neural Tangent Kernel converges. Building on this observation, we design a zero-shot surrogate model to estimate candidate performance without full training, significantly accelerating the architecture search process. Using this surrogate, we propose MZeQAS, a Monte Carlo Tree Search (MCTS)-based Zero-Shot Quantum Neural Architecture Search framework for VQAs. By integrating proxy-based performance estimation with MCTS exploration, MZeQAS efficiently discovers high-performing architectures. Experimental results demonstrate that MZeQAS outperforms existing approaches in terms of both search efficiency and solution quality, providing a scalable and effective framework for advancing VQA deployment on noisy intermediate-scale quantum devices.

Natural language is a powerful reasoning medium for language and vision-language models, but it is mismatched to the granularity of continuous control. Text and explicit subgoals operate at task-level granularity, whereas vision-language-action (VLA) policies must choose actions at a much finer temporal scale; a single reasoning step can therefore span many action chunks while remaining only weakly coupled to the action needed now. This suggests a different question for VLA: what should play the role of language? We argue that a useful VLA reasoning medium must be shareable across model instances, verifiable through downstream action improvement, and aligned with temporally extended control structure. Based on this view, we propose Continuous Reasoning for Vision-Language-Action. Our model first predicts continuous reasoning in the form of a structured set of continuous thoughts, then reuses them as shared context for chunk-structured action generation. Better action prediction alone does not certify good reasoning: if the same internal medium cannot be shared across model instances and independently verified through improved downstream control, the added latent may simply become a model-private shortcut that helps on seen behaviors without supporting generalizable control. We therefore instantiate continuous reasoning as a shared Gaussian latent interface and train it with a self-verification objective in which an exponential-moving-average teacher must successfully consume the student's reasoning when predicting target actions. Empirically, Continuous Reasoning improves LIBERO-PRO robustness and performs strongly on real robots, raising mean subtask success over π0.5 by 40.4% on TX-G2, an AgiBot G2-compatible variant, and 26.3% on HSR. This suggests that reasoning in VLA is less about extra tokens than about a shareable, verifiable internal language for action.

Test-time compute (TTC) scaling has emerged as a powerful paradigm for improving large language model (LLM) reasoning by allocating additional compute during inference, e.g., via multi-sample generation and verifier-based reranking. Existing TTC scaling strategies and reasoning scorers remain fragmented, evaluated under inconsistent protocols, and are rarely analyzed through the lens of quality-cost trade-offs. We introduce ThinkBooster, a unified framework for seamless test-time compute scaling of LLM reasoning, which consists of (i) a modular Python library implementing state-of-the-art TTC scaling strategy and scorer families, (ii) a benchmark that jointly evaluates performance and computational efficiency, and (iii) a deployable OpenAI-compatible proxy service that enables drop-in integration of adaptive reasoning into real-world applications. We further provide a demo visual debugger for inspecting the reasoning trajectories, intermediate selection decisions, and alternative reasoning paths. Empirical results on mathematical and coding tasks reveal the performance-compute trade-offs of TTC scaling strategies and scoring methods and demonstrate that ThinkBooster provides practical gains in real-world tasks. The code is available online under an MIT license.

While sparse autoencoders provide features more interpretable than individual neurons, reliably characterizing them remains challenging. We propose Query Lens, which extends Logit Lens to enable more comprehensive and faithful interpretations of sparse features. By jointly considering encoder-side key features and decoder-side value features, we identify both the inputs that activate a feature and the outputs it promotes. We also account for indirect, module-mediated effects that arise when the feature is processed by downstream modules, going beyond the direct effect captured by Logit Lens. In experiments, we find that Query Lens yields coherent token signatures for features that remain uninterpretable under Logit Lens. Finally, we propose the Subspace Channel Hypothesis, suggesting that downstream modules read features through layer-specific subspaces.

Self-supervised methods that learn representations and predict dynamics fully in the latent space, such as JEPA, have been shown to confuse slowly varying noise with the dynamical signals they aim to capture. Specifically, when noise features remain approximately constant within each trajectory, contrastive predictive objectives preferentially encode these features instead of the true latent variables governing the system. The learned representation then becomes dominated by trajectory-specific noise, so downstream performance degrades with noise strength and does not improve even as the number and duration of training trajectories increase. We argue that this failure is a property of the objective itself, shared by a long line of contrastive predictive objectives that sample negatives across trajectories. To illustrate this generality, we study the failure mode and its remedy in two settings: a standard SimCLR-style JEPA on a synthetic moving-dot dataset, and DySIB, a recently introduced method designed for extracting physically interpretable representations of dynamics, on movies of a rigid-body pendulum. When negatives are instead sampled within a single trajectory, the slow noise can no longer distinguish frames within that trajectory, removing the predictive shortcut. Training one encoder simultaneously on many such trajectories then forces it to encode the variables relevant for the dynamics, with longer trajectories yielding better representations even for strong slow noise. Our results point toward principles for designing contrastive predictive objectives in dynamical representation learning, especially for physical systems with noisy experimental observations.

Neural fields parameterize data as functions from coordinates to values, providing a unified framework for representation learning across modalities. Existing approaches are dominated by per-sample meta-learning, which scales poorly due to memory-intensive inner-loop optimization. The natural alternative -- feed-forward encoding -- typically introduces modality-specific assumptions, sacrificing the generality that makes learning with neural fields attractive. We argue that locality and hierarchy are useful priors for learning field representations that can be injected without compromising modality-agnosticism. We propose LH-NeF, a framework to learn general-purpose tokenized representations of continuous signals. A locality-preserving hierarchical encoder maps raw coordinate-value field observations to structured tokens, from which the field is reconstructed during training. By replacing meta-learning's inner loop with a single forward pass, LH-NeF uses 42$\times$ less memory and supports 133$\times$ larger batches than the strongest modality-agnostic baseline. Across images, 3D shapes, and climate fields, our learned representations match or exceed performance of modality-agnostic, modality-specific, and specialized generative neural field baselines on both reconstruction and downstream tasks.

Learned representations across models and modalities often exhibit striking structural similarities, suggesting shared underlying concept decompositions. However, concept alignment remains poorly defined: existing approaches optimize different objectives under the same terminology, obscuring what is actually aligned. We propose a unifying framework that decomposes alignment along two axes: what is aligned (representations vs. concepts) and at what level (instance-wise vs. distributional). This induces four corresponding properties -- instance-wise and distributional variants of translation and concept consistency -- and reveals precisely which of these guarantees existing methods provide. We further introduce \InterVenchA, an intervention-based benchmark that separately measures extraction quality, translation quality, and concept consistency. Through theory and experiments, we show that commonly assumed equivalences between alignment objectives fail in practice: optimizing one property does not reliably recover the others, and purely unsupervised objectives fail to recover meaningful instance-level alignment. We then propose the Coupled Sparse Autoencoder (CoSAE), which jointly enforces complementary alignment objectives. Strong alignment emerges only in this regime. Surprisingly, as little as 0.1\% paired data is sufficient to recover instance-level alignment when anchoring distributional objectives. Overall, our results show that concept alignment is fundamentally multi-objective: it must be defined, measured, and optimized as such.

Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored. Drawing inspiration from self-supervised learning (SSL), we introduce a framework for jointly evaluating the representation and generation capabilities of diffusion models. Specifically, we decompose features into invariant and residual components and derive the Invariant Contamination Ratio (ICR), a Fisher-based metric that quantifies how residual variation contaminates invariant signal in feature space. We use this framework to analyze both discriminative and generative behavior of diffusion models. On the representation side, we find that invariance peaks at intermediate noise levels, which also yield the best downstream classification performance. On the generative side, we study how training transitions from genuine generalization to memorization in data-limited regimes, and show that ICR serves as a sensitive training-time indicator of early learning: increasing residual energy along Fisher directions marks the onset of memorization, detectable from training features alone without external evaluators or held-out test sets. Overall, our results show that diffusion models can be monitored from a self-supervised perspective through the geometry of their learned representations.

Disentanglement, the separation of factors of variation in data using neural networks, remains a long-standing challenge in machine learning. Prior work has addressed this problem with variational autoencoders and generative adversarial networks that incorporate ideas from variational inference and information-theoretic constraints. In contrast to methods that rely on continuous representations, we propose a design that treats disentangled representations as symbolic structures, motivated by the compositional relationships among the concepts that make up samples from a distribution. However, learning discrete symbolic structures with neural networks while maintaining differentiability is difficult and often requires complex architectures. To address this, we introduce an unsupervised learning algorithm that uses holographic reduced representations (HRR) for neural disentanglement. We show that the HRR unbinding operation provides an inductive bias for separating factors and yields competitive results against baselines, as measured by latent traversals and disentanglement metrics. We complement these empirical findings with an information-theoretic analysis of the HRR unbinding channel. We prove that unbinding induces approximately independent symbol-value pairs and derive a per-slot capacity bound that quantifies how many distinct symbolic concepts can be reliably encoded, giving a quantitative account of the inductive bias toward disentanglement. The resulting representations differ from standard autoencoder-based models, in that their latent units are vectors that are summed together, rather than scalar dimensions of a low-dimensional latent vector. We show that this HRR representation is more robust to noise than other disentangled representations and maintains reconstruction quality across a range of SNRs.

We propose an unsupervised method of resolving slang, unique entities, and folklore from online communities by isolating words in the lexicon that have the highest magnitude of semantic shift. Semantic shift is defined as the evolution of a word's encoded representation as a result of fine-tuning a pretrained Large Language Model (LLM) on a community-specific text corpus. This value is inversely proportional to the cosine similarity between the base model's encoded representation of a word, and a fine-tuned model's encoded representation. We fine-tune the DistilRoBERTa model on text corpora collected from 3 Reddit subreddits (r/Technology, r/Gaming, r/WorldofWarcraft), model a distribution of cosine similarity over the lexicon, and show that one can successfully resolve words that have unique significance to the community by pulling data in the bottom 10-percentile. In contrast, we show that data in the top 10-percentile consist of words that carry relatively universal semantics.

Displacement time series from Global Navigation Satellite Systems (GNSS) are essential for a wide range of applications, including monitoring tectonic crustal deformations and investigating the different stages of the earthquake cycle. Machine learning methods have proven promising for GNSS applications; however, most remain fully supervised. This creates a bottleneck as labeled data are scarce, even though large amounts of unlabeled GNSS data are freely available. We present GNSS-FM, a self-supervised foundation model for daily GNSS time series. The model uses a dual-stream input combining displacement and velocity-like increments, and is pretrained using a masked latent prediction objective with vector-quantized targets adapted from wav2vec 2.0, with several modifications for geodetic data. Pretrained on data from over 17,000 globally distributed GNSS stations, an analysis of the learned codebook suggests that the representations capture the main signal types in GNSS displacement data, including seismic offsets, tectonic drift, and seasonal patterns. The foundation model is later fine-tuned on two downstream tasks, namely 90-day displacement forecasting and seismic step localization, where it outperforms strong task-specific baselines in both cases. These results show that self-supervised pretraining is a promising approach for GNSS time series analysis.

As large language models are increasingly deployed in high-stakes settings, there is a growing need for tools that audit not only model outputs but also the internal computations that produce them. Circuit analysis is a central approach in mechanistic interpretability, but it is typically target-conditioned, explaining a single prompt paired with a chosen completion. This target-conditioned setup can obscure heterogeneity across a model's continuation distribution. We introduce distribution-level unsupervised feature discovery, which clusters sampled continuations using both semantic content and sequence-level mechanistic attributions, without manually specifying target outputs. Our method represents each continuation with a semantic embedding and a prefix-to-continuation attribution signature, then optimizes a rate-distortion objective that trades off semantic coherence, mechanistic consistency, and cluster granularity. Across clustering and steering analyses, the discovered clusters expose continuation modes that single-view baselines miss and provide interventional evidence that cluster signatures correspond to actionable mechanistic factors. Overall, our approach complements circuit analysis and behavioral evaluation by providing a scalable audit of the mechanisms underlying a model's continuation distribution.

Although Sparse Autoencoders (SAEs) have mitigated the opacity of large language models (LLMs) by decomposing dense representations into sparse features, explaining these features still remains a central challenge. Current explanation methods, however, typically operate within an open-loop paradigm, failing to leverage mechanistic feedback for further refinement. In this paper, we propose SAEExplainer, a training framework utilizes activation scores as an objective reward signal to train the model for self-correction and iterative bootstrapping. By iteratively verifying and correcting foundational explanations through a two-round optimization process, SAEExplainer achieves continuous improvement in its explanatory capabilities. This mechanism significantly reduces explanation hallucinations and reinforces causal triggering patterns. Extensive experiments demonstrate our approach improves upon established baselines across most metrics, especially in causal triggering and discriminative activation.

Sophisticated generative speech technology can undermined the reliability of voice biometrics. While spoofing detection systems excel when assessed under in-domain conditions, generalisation to out-of-domain settings is often poor. In this paper, we show that such issues could be caused by speaker bias, where models learn individual voice traits rather than markers of manipulation or generation. We propose a teacher-student framework for speaker-invariant spoofing detection that disentangles identity without requiring speaker labels. We leverage a pre-trained speaker recognition teacher to guide a student model via a gradient reversal layer. To control the balance between suppressing cues related to voice identity with the preservation of those related to spoofing detection, we integrate a Variational Information Bottleneck. Evaluations across nine datasets show our model achieves a 25.7% relative reduction to the EER compared to the MHFA baseline.

Recent advances in video multimodal models have significantly improved VideoQA performance. However, these systems often rely on spurious statistical correlations rather than answer-relevant causal evidence, resulting in unfaithful and brittle reasoning, especially in complex real-world scenarios. Existing methods either rely on cross-modality correlations, costly curated training resources, or insufficient causal assumptions and constraints, and typically operate at the time-interval level. As a result, they fail to explicitly disentangle causal visual cues from confounders and provide limited fine-grained evidence localization. To address this issue, we propose a Counterfactual Reasoning framework for fine-grained Evidence Disentanglement (CREDiT). CREDiT formulates the VideoQA process using a structural causal model and learns cross-modality representations that are explicitly decomposed into causal and non-causal components under independence and minimality constraints. To facilitate faithful disentanglement, we introduce feature-level causal interventions and construct counterfactual inputs that approximate causal effects while suppressing non-causal correlations. Extensive experiments on NExT-GQA, SportsQA, and SPORTU-video demonstrate that CREDiT consistently improves answer accuracy and reasoning reliability across both generic and complex sports scenarios, leading to more trustworthy VideoQA systems.

Omni-modal retrieval promises a single embedding space for text, image, video, document, and audio inputs, but building such a unified retriever is difficult since these modalities differ in data distribution, architecture, and optimization dynamics. In this work, we present Conan-embedding-v3, a decouple--fuse--recover framework for omni-modal retrieval. Conan-embedding-v3 first trains modality specialists independently and fuses their task vectors into a single dense backbone, a strategy we call Decoupled Specialist Fusion. We show that this fusion composes visual, video, and document retrieval capabilities, but also exposes a failure mode for projector-based modalities: when audio is attached through an external encoder and projector, fusing the backbone leaves the projector calibrated to the audio-specialist backbone, causing a large audio retrieval regression despite copying all audio-specific modules unchanged. We call this failure Projector Drift. To repair it, Conan-embedding-v3 applies Projector Recovery (i.e., full-parameter fine-tuning of the projector while keeping the backbone frozen) followed by balanced multi-modal rehearsal. The resulting model supports these retrieval pathways in one backbone, achieving 74.9 scores on MMEB while obtaining 55.61 on the 30-task MAEB audio suite.

Causal disentanglement from soft interventions is identifiable under the assumptions of linear interventional faithfulness and availability of both observational and interventional data. Prior work has focused on unstructured observations without leveraging known relational context among measured entities. In many scientific applications, however, the measured variables come with an observed interaction network that provides structured context, such as protein-protein interactions and pathway-gene membership. We propose GraCE-VAE, a graph-aware causal discrepancy variational autoencoder that treats pathway-level information as an auxiliary view of the latent causal programs. The graph neural network encoder conditions on this auxiliary pathway view and the biological graph to improve amortized inference, while the causal decoder remains a latent SCM with soft interventions. Assuming samples are i.i.d. within each intervention regime, we show that GraCE-VAE inherits the identifiability guarantees of causal discrepancy VAEs and identifies the latent causal graph and intervention targets up to the standard equivalence class. Experiments on three CRISPR perturbation datasets demonstrate that leveraging structured biological context improves prediction of interventional outcomes, including unseen perturbation combinations.

Self-supervised learning (SSL) learns representations from massive unlabeled data, yet the resulting models typically operate as black boxes, necessitating domain-specific explanations. We introduce KREPES, a unified framework to analytically interpret the learned representations of SSL objectives, including SimCLR, BYOL, and VICReg. By bridging empirical neural tangent kernel approximations of neural networks with the Representer Theorem for kernels, we express the learned latent space directly via "Representer Landmarks", which are the representations of influential unlabeled training examples. We introduce novel metrics, "Sample-Specific Influence Score", "Concept-Conditioned Influence Score" and "Feature Alignment Gap", to quantify the transparency of the learned representations. KREPES enables direct audit of the latent space without supervision, for example, revealing an algorithmic bias in the Adult-1M dataset where SSL uses demographic proxies for income. Finally, to ensure scalability to benchmarks with 1M+ samples (ImageNet-1K, Adult-1M), KREPES introduces a novel Nyström approximation-based analytical inference framework for SSL objectives.

The effectiveness of self-supervised learning (SSL) for physiological time series depends on the ability of a pretraining objective to preserve information about the underlying physiological state while filtering out unrelated noise. However, existing strategies are limited due to reliance on heuristic principles or poorly constrained generative tasks. To address this limitation, we propose a pretraining framework that exploits the information structure of a dynamical systems generative model across multiple time-series. This framework reveals our key insight that class identity can be efficiently captured by extracting information about the generative variables related to the system parameters shared across similar time series samples, while noise unique to individual samples should be discarded. Building on this insight, we propose PULSE, a cross-reconstruction-based pretraining objective for physiological time series datasets that explicitly extracts system information while discarding non-transferrable sample-specific ones. We establish theory that provides sufficient conditions for the system information to be recovered, and empirically validate it using a synthetic dynamical systems experiment. Furthermore, we apply our method to diverse real-world datasets, demonstrating that PULSE learns representations that can broadly distinguish semantic classes, increase label efficiency, and improve transfer learning.

Recent progress in geospatial foundation models highlights the importance of learning general-purpose representations for real-world locations, particularly points-of-interest (POIs) where human activity concentrates. Existing approaches, however, focus primarily on place identity derived from static textual metadata, or learn representations tied to trajectory context, which capture movement regularities rather than how places are actually used (i.e., POI's function). We argue that POI function is a missing but essential signal for general POI representations. We introduce Mobility-Embedded POIs (ME-POIs), a framework that augments POI embeddings derived, from language models with large-scale human mobility data to learn POI-centric, context-independent representations grounded in real-world usage. ME-POIs encodes individual visits as temporally contextualized embeddings and aligns them with learnable POI representations via contrastive learning to capture usage patterns across users and time. To address long-tail sparsity, we propose a novel mechanism that propagates temporal visit patterns from nearby, frequently visited POIs across multiple spatial scales. We evaluate ME-POIs on five newly proposed map enrichment tasks, testing its ability to capture both the identity and function of POIs. Across all tasks, augmenting text-based embeddings with ME-POIs consistently outperforms both text-only and mobility-only baselines. Notably, ME-POIs trained on mobility data alone can surpass text-only models on certain tasks, highlighting that POI function is a critical component of accurate and generalizable POI representations.

Computational molecular representations underpin virtual screening, property prediction, and materials discovery. Conventional fingerprints are efficient and deterministic but lose structural information through hash-based compression, particularly at low dimensionalities. Learned representations from graph neural networks recover this expressiveness but require task-specific training and substantial computational resources. Here we introduce hyperdimensional fingerprints (HDF), which replace the learned transformations of message-passing neural networks with algebraic operations on high-dimensional vectors, producing deterministic molecular representations without any training. Across diverse property prediction benchmarks, HDF outperforms conventional fingerprints in the majority of tasks while exhibiting greater consistency across datasets and models. Crucially, HDF embeddings preserve molecular similarity faithfully: at 32 dimensions, distances in HDF space achieve a 0.9 Pearson correlation with graph edit distance, compared to 0.55 for Morgan fingerprints at equivalent size. This structural fidelity persists at low dimensions where hash-based methods degrade, allowing simple nearest-neighbor regression to remain predictive with as few as 64 components. We further demonstrate the practical impact in Bayesian molecular optimization, where HDF-based surrogate models achieve substantially improved sample efficiency in regimes where Morgan fingerprints perform comparably to random search. HDF thus provides a general-purpose, training-free alternative to conventional molecular fingerprints, suggesting that the information loss long accepted as inherent to fixed-length fingerprints is a limitation of the hash-based encoding scheme rather than the fingerprint paradigm itself.

Many operations on sensory data -- comparison, memory, retrieval, and reasoning -- are naturally expressed over discrete symbolic structures. In language this interface is given by tokens; in audio, it must be learned. Existing audio tokenizers rely on quantization, clustering, or codec reconstruction, assigning tokens locally, so sequence consistency, compactness, length control, termination, and edit similarity are rarely optimized directly. We introduce PairAlign, a framework for compact audio tokenization through sequence-level self-alignment. PairAlign treats tokenization as conditional sequence generation: an encoder maps speech to a continuous condition, and an autoregressive decoder generates tokens from BOS, learning token identity, order, length, and EOS placement. Given two content-preserving views, each view's sequence is trained to be likely under the other's representation, while unrelated examples provide competing sequences. This gives a scalable surrogate for edit-distance preservation while discouraging many-to-one collapse. PairAlign starts from VQ-style tokenization and refines it with EMA-teacher targets, cross-paired teacher forcing, prefix corruption, likelihood contrast, and length control. On 3-second speech, PairAlign learns compact, non-degenerate sequences with broad vocabulary usage and strong cross-view consistency. On retrieval tests, it preserves edit-distance search while reducing archive token count by 55%. A continuous-sweep probe shows lower local overlap than a dense geometric tokenizer, but stronger length control and bounded edit trajectories under 100 ms shifts. PairAlign is a sequence-symbolic predictive learner: like JEPA-style objectives, it predicts an abstract target from another view as a learned variable-length symbolic sequence, not a continuous latent.

Large language models succeed by combining large-scale pretraining with meaningful discrete tokens. In molecular machine learning, SMILES is widely used as a token representation, but it is primarily a linearization format for molecular graphs rather than a semantic decomposition of chemistry. We propose VQ-Atom, a semantic tokenization framework that assigns discrete atom-level tokens based on local chemical environments via vector quantization. Unlike SMILES tokens, VQ-Atom tokens encode graph-local chemical context and are aligned with molecular structure. On protein-cold drug--target interaction prediction using the KIBA dataset, VQ-Atom substantially improves global ranking performance, achieving AUROC of 0.79 while substantially outperforming both SMILES-based and continuous molecular representations under an identical downstream architecture. Furthermore, VQ-Atom enables approximately 3 times faster downstream training than continuous atom-level representations by replacing per-atom continuous features with reusable discrete tokens. These results suggest that molecular tokenization is not merely a preprocessing step, but a central design choice. In particular, well-structured tokens can encode substantial chemical semantics, reducing the burden on downstream learning. VQ-Atom can be interpreted as defining a molecular language, where tokens correspond to chemically meaningful atomic environments, suggesting that token design may constitute an additional axis of machine learning research alongside architecture, objectives, and optimization.

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space. Freshly introduced geometry-aware manifold methods do learn such a geometry, but require labelled class centroids together with prescribed cyclic or sequential structure. These assumptions restrict where manifold steering can be applied, since existing constructions require labelled centroids and compatible boundary conditions. We recast manifold steering more broadly as \textbf{Riemannian geodesic computation} on activation space, recovering linear and labelled-spline steering as geodesics under particular choices of metric. A principled metric within this framework is the output-space Hellinger distance pulled back to activations; we approximate this with a learned encoder trained on output distances over a small concept-token schema - no per-prompt labels, no topology prior, and no per-task curve fitting. Empirically, the method reliably drives the model onto the target class across all tasks in a standard four-task language-model arithmetic benchmark, while following more behaviourally natural trajectories than baselines on smaller output spaces. We thereby provide a unified Riemannian framework for manifold steering together with a schema-supervised, label-free instantiation that operates without labelled centroids or prescribed boundary conditions.

Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.

Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning. Conventional algorithms optimize in the space of computationally intractable completely positive matrices or relax the problem to the space of doubly nonnegative matrices that scale with sample size in a way rendering them impractical for large data sets. Some of these methods also impose a row sum constraint, such as double stochasticity. Row sum constraints have the added advantage of being shift-invariant, in the context of manifold tiling. Constraints on the row sum of output similarity matrices require nontrivial online learning rules. Addressing these needs, we propose a versatile online biologically plausible learning algorithm capable of learning sparse shift-invariant representations, useful for clustering, manifold tiling, or sparse coding, depending on the data structure.

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose Entropic Optimal Transport (EOT) eigenmaps, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align them in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We analyze a generative model in which two observed high-dimensional datasets share latent variables supported on a common low-dimensional manifold, while each dataset is subject to translation, geometric distortion, orthogonal nuisance structure, and noise. In a large-sample, high-dimensional regime, we prove that the EOT plan concentrates around a population kernel on an effective manifold determined by the geometric mean of the distortions, with invariance to translations, orthogonal nuisance structure, and noise. Subsequently, we relate our embedding to eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios.

When predictors are statistically dependent, the appropriate definition of feature importance depends on the operational goal. Conditional-incremental measures are well-suited for feature selection, acquisition, and compression, where shared predictive information is treated as redundancy. For post-hoc interpretation, however, the goal is often to attribute predictive signals across correlated measurement channels. We introduce Disentangled Feature Importance (DFI), a population-level attribution framework for this setting. DFI maps covariates to an independent latent representation under a specified entropic optimal transport geometry, computes latent importance, and attributes it back to the original covariates through barycentric sensitivities. We show that broad conditional-incremental FI functionals target conditional incremental predictive value under squared-error loss, and therefore answer a different question from attribution of shared predictive signal under dependence. Under fixed transport cost, reference law, and regularization level, DFI defines a well-specified family of estimands. Latent scores admit a functional ANOVA interpretation, and in the Gaussian linear case, the attributed DFI recovers the classical $R^2$ decomposition for correlated regressors. We derive influence-function-based inference under nuisance-rate and smoothness conditions, and show in simulations and an HIV-1 neutralization-resistance analysis that DFI yields stable, interpretable, uncertainty-quantified attributions of shared predictive signal.

We find that current sentence-embedding models produce outputs with a consistent bias: every embedding $e$ decomposes as $\tilde e + μ$, where the mean $μ$ is near-identical across all sentences. We study two training-free corrections -- subtracting $μ$ directly (R1), or projecting each embedding off the mean direction (R2) -- and show, via a first-order error-propagation argument, that R2 cancels the parallel component of mean-estimation error that R1 retains. Across 38 models on the Massive Multilingual Text Embedding Benchmark (MMTEB)~\citep{MMTEB}, R2 yields consistent classification gains (paired $\bar t = 3.31$, 29 of 38 models with $t>2$, zero losses), and the per-model mean norm $\Vertμ\Vert$ correlates with which models benefit most. A nine-method dose-response ablation on five models further reveals that mild single-direction removal helps, but full principal component analysis (PCA) whitening hurts every model we test, and that R2 and All-but-the-Top with depth one agree within $0.18$ pp downstream despite weak geometric alignment between $\hatμ$ and the centered top principal component.

Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge. While CBMs use supervision to align activations with human-labeled concepts, SAEs rely on sparse coding to uncover emergent ones. We show that both paradigms instantiate the same geometric structure: each learns a set of linear directions in activation space whose nonnegative combinations form a concept cone. Supervised and unsupervised methods thus differ not in kind but in how they select this cone. Building on this view, we propose an operational bridge between the two paradigms. CBMs provide human-defined reference geometries, while SAEs can be evaluated by how well their learned cones approximate or contain those of CBMs. This containment framework yields quantitative metrics linking inductive biases -- such as SAE type, sparsity, or expansion ratio -- to emergence of plausible\footnote{We adopt the terminology of \citet{jacovi2020towards}, who distinguish between faithful explanations (accurately reflecting model computations) and plausible explanations (aligning with human intuition and domain knowledge). CBM concepts are plausible by construction -- selected or annotated by humans -- though not necessarily faithful to the true latent factors that organise the data manifold.} concepts. Using these metrics, we uncover a ``sweet spot'' in both sparsity and expansion factor that maximizes both geometric and semantic alignment with CBM concepts. Overall, our work unifies supervised and unsupervised concept discovery through a shared geometric framework, providing principled metrics to measure SAE progress and assess how well discovered concept align with plausible human concepts.

While Mechanistic Interpretability has identified interpretable circuits in LLMs, their causal origins in training data remain elusive. We introduce Mechanistic Data Attribution (MDA), a scalable framework that employs Influence Functions to trace interpretable units back to specific training samples. Through extensive experiments on the Pythia family, we causally validate that targeted intervention--removing or augmenting a small fraction of high-influence samples--significantly modulates the emergence of interpretable heads, whereas random interventions show no effect. Our analysis reveals that repetitive structural data (e.g., LaTeX, XML) acts as a mechanistic catalyst. Furthermore, we observe that interventions targeting induction head formation induce a concurrent change in the model's in-context learning (ICL) capability. This provides direct causal evidence for the long-standing hypothesis regarding the functional link between induction heads and ICL. Finally, we propose a mechanistic data augmentation pipeline that consistently accelerates circuit convergence across model scales, providing a principled methodology for steering the developmental trajectories of LLMs.

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at $t=0.5$ if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

Data collected from the physical world is always a combination of multiple sources: an underlying signal from the physical process of interest and a signal from measurement-dependent artifacts from the sensor or instrument. This secondary signal acts as a confounding factor, limiting our ability to extract information about the physics underlying the phenomena we observe. Furthermore, it complicates the combination of observations in heterogeneous or multi-instrument settings. We propose a deep learning framework that leverages overlapping observations, a dual-encoder architecture, and a counterfactual generation objective to disentangle these factors of variation. The resulting representations explicitly separate intrinsic signals from sensor-specific distortions and noise, and can be used for counterfactual view generation, parameter inference unconfounded by measurement distortions, and instrument-independent similarity search. We demonstrate the effectiveness of our approach on astrophysical galaxy images from the DESI Legacy Imaging Survey (Legacy) and the Hyper Suprime-Cam (HSC) Survey as a representative multi-instrument setting. This framework provides a general recipe for scientific and multi-modal self-supervised pretraining: construct training pairs from overlapping observations of the same physical system, treat sensor- or modality-specific effects as augmentations, and learn invariant representations through counterfactual generation.

Decentralized multi-agent swarm coordination on resource-constrained edge platforms remains fundamentally bottlenecked by the exponential scaling of joint action spaces and high-latency communication overhead. This paper introduces the Swarm Policy Interference Network (SPIN) framework, an architectural paradigm that bypasses these limitations by modeling swarm topologies as a compressed tensor network. We factorize the joint policy tensors of local multi-agent cliques into Matrix Product State (MPS) chains, reducing the computational complexity of evaluation from an exponential $O(n^m)$ wall to a strictly linear $O(m \cdot n \cdot χ^2)$ constraint. To bridge local continuous spatial geometry with this discrete algebraic backend without requiring power-intensive online training loops, we introduce a decoupled, hybrid neuro-symbolic control pipeline. Local multi-layered neural networks operate as structural coordination encoders, pre-trained offline to nonlinearly map hand-engineered geometric descriptors into abstract environmental target measures. At runtime, edge agents execute instantaneous behavioral adaptations by applying the Radon-Nikodým derivative directly as a zero-shot importance-reweighting filter. We validate the framework within a discrete-time multi-agent simulation sandbox spanning tracking, decentralized dispersion/area coverage, and multi-goal coordination regimes. Qualitative telemetry demonstrates that the integrated pipeline achieves stable target-directed motion, anti-collapse spatial spreading under decentralized constraints, and structured subgroup formation across multiple targets, providing a mathematically grounded route to tractable, low-power edge swarm intelligence.

Self-healing smart grids can quickly adjust their network configuration during outages to minimize power disruptions. During an outage, several actions can be taken, such as network reconfiguration through switching operations and emergency load shedding. However, traditional machine learning methods for outage mitigation are not well suited for smart grids due to their slow response time and high computational cost. To address these challenges, recent studies have explored reinforcement learning to automatically perform network reconfiguration. In these approaches, the control policy is typically modeled using a graph neural network (GNN). However, conventional GNNs operate in the spatial domain and may fail to capture important relationships in the frequency domain. Frequency-domain information is particularly useful for modeling global structural patterns and system-wide interactions in power networks. In this paper, we propose a spectral graph reinforcement learning framework for outage management in distribution networks to enhance system resilience. Our model learns the optimal power restoration policy using a spectral graph neural network. We evaluate the proposed method on three modified IEEE test systems: the 13-bus, 34-bus, and 123-bus networks. Experimental results show that our approach achieves near-optimal performance in real time and generalizes well across a wide range of outage scenarios.

Offline reinforcement learning requires careful conservatism to mitigate distribution shift, yet most existing methods apply a fixed penalty uniformly across all states regardless of local data coverage. We present UNIQ (Uncertainty-Informed Quantile), an offline RL method that introduces state-adaptive conservatism through conformally calibrated uncertainty estimation. Built on the Implicit Q-Learning (IQL) backbone, UNIQ trains a multi-expectile value ensemble, computes distribution-free uncertainty estimates using split conformal prediction, and maps the resulting signal to a state-dependent expectile that relaxes conservatism in well-covered regions while strengthening it in uncertain regions near the data frontier. On D4RL MuJoCo benchmarks, UNIQ consistently improves over IQL, with the largest gains observed on Walker2d and replay-heavy tasks. At the same time, UNIQ operates at near-IQL memory cost (approximately 250 MB peak VRAM), providing roughly a 10x reduction compared to EDAC. Rather than pursuing overall state-of-the-art performance, we position UNIQ as a practical mechanism contribution that improves the performance-efficiency trade-off in offline reinforcement learning.

LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility. We identify a data-induced failure mode, PhysHack, in which the assemblies satisfy physical-validity constraints while producing structures that are geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only a small fraction of the training data while improving physically grounded LEGO assembly generation. Building on the selected trajectories, we introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards. Our results show that physical validity alone is an insufficient proxy for reliable physical reasoning: models can learn to generate valid structures without preserving semantic or geometric fidelity. Experiments across model backbones and test-time scaling settings demonstrate that PVPO improves structural and semantic alignment, physical validity, structural stability, and calibration, while reducing reliance on extensive post-hoc rejection sampling. In particular, results on calibration show that PVPO mitigates PhysHack by making test-time selection more predictive of semantic and structural quality.

State-of-the-art GRPO-style methods for speech-aware large language model post-training suffer from coarse credit assignment, broadcasting the same terminal-reward advantage to every token in a response. This ignores useful structure within rollout batches, where speech-conditioned completions often share prefixes before diverging at important decisions. We propose Low-rank Exploration with Adaptive Forking (LEAF), a retrospective tree-based RL method that recovers this structure without online branching or additional decoding. LEAF samples complete responses, selects high-surprisal boundaries, groups responses by shared prefixes, and assigns span-level advantages using descendant rewards. We theoretically justify LEAF's span-level credit assignment and boundary-selection design. Empirically, LEAF improves over GRPO across speech question answering and speech translation benchmarks under the same rollout and low-rank adaptation budget. Notably, smaller LEAF-trained models outperform current state-of-the-art, full-parameter baselines.

Although multi-objective reinforcement learning (MORL) is central to aligning large language models with complex human preferences, the prevailing practice of static weighted summation overlooks a more fundamental phenomenon: reward learning is markedly asynchronous across objectives. Well-learned dimensions quickly produce homogeneous, low-variance signals whose residual noise contaminates the aggregated reward (in GRPO) or occupies a fixed share of the advantage budget (in GDPO), interfering with the scarce yet high-value signals carried by under-learned dimensions. To address this asynchrony, we propose Stage-Aware Dynamic Weighting (SAW), a lightweight, algorithm-agnostic dynamic weighting mechanism. SAW utilizes the coefficient of variation (CV) as a scale-invariant proxy for real-time informativeness, reweighting each dimension's reward or advantage contribution by its relative informativeness within the batch. Unlike gradient-based methods that require multiple forward and backward passes, SAW relies solely on batch-level statistics, introducing nearly negligible computational overhead. Experiments on tool-calling and text summarization tasks demonstrate that SAW consistently improves both training efficiency and final performance under both GRPO and GDPO frameworks, confirming it as a general-purpose plug-in for multi-reward LLM alignment. Our code is available at https://github.com/Zhaolutuan/SAW

The challenge with active learning algorithms is the uncertainty of the statistical distribution of unlabeled data, making it difficult to choose the best hand-crafted strategy. To address this, we introduced Contextual Adaptive Active Learning (CAAL). In CAAL, each "arm" represents a hand-crafted strategy. Unlike existing frameworks that select strategies based only on feedback from labeled data, we dynamically choose strategies for labeling batches of data using reward prediction with external context information. This general framework allows for customization with domain knowledge to design more effective rewards and context candidates. In addition, we experimentally show that CAAL outperforms the existing baseline adaptive strategy on public datasets using our reward and context design. Our results are consistent regardless of batch size in each iteration.

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

Multi-agent large language model (LLM) systems often fail to reliably outperform a single strong model equipped with best-of-N sampling. We argue that a core source of this instability is ill-posed equilibrium selection: current systems specify what information agents share, but not which coordination convention should be selected. We formalize a broad class of such systems as discounted incomplete-information Markov games and show that two common pathologies, oscillation between competing conventions and drift across them, can both induce unstable learning and linear Bayesian regret. To obtain a well-posed target, we introduce the Heterogeneous Quantal Response Equilibrium (HQRE), an entropy-regularized equilibrium concept with agent- and state-dependent temperatures. Under a monotonicity condition, HQRE is unique, admits linearly convergent mirror updates, and yields bounded Bayesian regret; the same condition yields rollout-measurable stability diagnostics. We instantiate this objective in two algorithms: DICE-PC, which coordinates frozen models through prompt-control actions, and DICE-FT, which performs parameter-efficient mirror fine-tuning. Across eleven benchmarks in four domains, DICE improves accuracy-cost trade-offs over strong within-class baselines; on reasoning and planning tasks, DICE-PC improves by 4.3 percentage points on average and DICE-FT by 8.5 points.

Reinforcement Learning from Verifiable Rewards (RLVR) has recently become a key paradigm for improving the reasoning abilities of Large Language Models (LLMs), yet it remains limited by sparse binary rewards and its ignorance of model-internal uncertainty. In this paper, we propose ConSteer-RL, a simple yet effective framework that integrates token-level confidence signals derived from model log-probabilities into RLVR training. Specifically, building upon the Group Relative Policy Optimization (GRPO) framework, we construct a confidence-aware reward by aggregating per-token probabilities into a scalar confidence score and incorporating it into an awareness-based reward shaping mechanism that penalizes overconfident errors while reinforcing correct and confident reasoning. Experimental results demonstrate that ConSteer-RL consistently outperforms strong GRPO baselines, achieving average improvements of 2.3%-4.0% across different model scales.

Peer-referral recruitment systems such as respondent-driven sampling are critical for studying and intervening on hidden populations affected by infectious diseases. To accelerate recruitment, public health agencies must adaptively allocate limited referral resources across multiple rounds, where current decisions shape both the number and the covariates of future recruits. Prior work makes this problem tractable by assuming that referrals are drawn i.i.d.\ from a homogeneous population, an assumption that ignores the homophily and shared context that drive real peer recruitment. We instead consider a more realistic model in which both referral capacity and the covariates of newly referred individuals are conditioned on the referrer, learned from data with a censored count model and a conditional generative model. The resulting planning problem is challenging because each candidate allocation induces a different distribution over future recruits. We propose \emph{Generative Frontier Planning} (GFP), a model-based planner that replaces per-step Monte-Carlo sampling with a deterministic backup over a latent covariate-coverage value surrogate. The surrogate is designed so that the expected value of the next frontier depends on the offspring generative model only through finite-dimensional summaries that are amortized offline, and so that the resulting per-round objective is monotone with diminishing returns. Together, these two properties make planning tractable: the deterministic backup eliminates Monte-Carlo sampling, and the diminishing-returns structure lets a marginal greedy allocation achieve a \((1-1/e)\)-approximation for the per-round problem. On a simulation environment calibrated to a real respondent-driven sampling dataset, GFP outperforms random, reinforcement-learning, and i.i.d.\ dynamic-programming baselines across four discount factors.

Personalized decision-making in multi-objective bandits requires learning user-specific trade-offs among competing objectives. Since arm utility depends on both unknown rewards and unknown preferences, existing methods infer preferences only from utility feedback, entangling preference learning with reward exploration. In practice, however, users often reveal their priorities through proactive conversational queries (e.g., "cheap and clean hotel"), yet this structured signal is not leveraged. We formalize a proactive query-based framework in which user queries provide structured preference signals. Modeling these signals via a Plackett-Luce subset choice model, we show that query-only learning is insufficient due to a fundamental shift-invariance barrier. To resolve this, we introduce MO-PQUCB, a hybrid algorithm that integrates query-based preference anchoring with bandit feedback through shift-invariant regularization and dual-exploration UCB. We prove that proactive queries accelerate preference estimation and yield improved regret scaling over prior preference-aware MO-MAB methods. Under corrupted queries, we further characterize statistical limits and design a robust estimator achieving near-optimal performance when the corruption is sparse. Experiments validate both theoretical and practical gains.

Unmanned aerial vehicles (UAVs) are increasingly being deployed in logistics, service robotics, and other real-world applications, creating a growing demand for autonomous payload acquisition and delivery. Existing approaches typically assume pre-attached payloads or rely on specialized grippers, leaving versatile end-to-end aerial delivery largely unresolved, where different payloads induce highly variable flight dynamics, requiring a single policy to adapt online without manual calibration or explicit system identification. To this end, we study \textbf{A}utonomous \textbf{A}erial Manipulation via \textbf{Co}ntextual \textbf{Co}ntrastive Meta Reinforcement Learning (\textbf{\textit{Aco2}}), a fully autonomous aerial delivery setting in which a quadrotor equipped with a lightweight hook continuously picks up, transports, and delivers diverse handle-equipped objects between randomized locations, all without human intervention. First, we design a contextual observation encoder that infers a compact latent context from recent interaction history, enabling the policy to adapt online to payload-dependent dynamics. To further improve the quality of this context, we introduce a contrastive objective that structures the context embedding around task-relevant variations, improving generalization across diverse payloads without requiring explicit system identification. Trained entirely in simulation with extensive domain randomization, \textit{Aco2} can be directly deployed on a physical quadrotor without real-world fine-tuning.

We present an online reinforcement learning (RL) algorithm for fine-tuning flow-matching policies in continuous-control problems. Our key insight is to view RL-based policy improvement as a transport of action densities towards regions of high reward, which naturally aligns with the transport formulation of flow matching models. Prior methods either approximate the current or optimal policy distribution or resort to distillation, which introduces biased gradients or sacrifices multimodal modeling capacity. In contrast, our approach for RL with Density Transport, which we name \emph{RLDT}, constructs a transport field from a maximum-entropy RL objective using Stein Variational Gradient Descent (SVGD). Then, it finetunes a pretrained flow matching policy to align with this field. Training with this alignment objective is nontrivial because flow-matching policies generate actions via a multi-step process, making direct gradient-based optimization challenging. To overcome this challenge and stabilize training, we approximate policy actions from intermediate denoising steps via expected-target estimation. This allows the transport-field update to propagate into the network parameters without unstable backpropagation through time. Experimental results demonstrate that RLDT outperforms competitive baselines in reward quality and convergence speed. This performance holds across diverse continuous-control tasks, encompassing both dense and sparse rewards, as well as state- and vision-based long-horizon robot manipulation. The project webpage is \href{https://rpfey.github.io/rldt/}{https://rpfey.github.io/rldt/}.

Agent skills extend language-model agents with task-specific procedures, scripts, and references, but the tasks and environments they target continually change. Existing methods improve skills in bounded runs and retain only the final artifact, discarding the decision history that later agents need to interpret prior revisions, evaluations, and rejected alternatives. We introduce SkillHone, a harness for continual agent skill evolution grounded in persistent decision history. SkillHone pairs skill revisions with evaluation-side evidence that supplies practice feedback, recording structured histories of diagnoses, revisions, evidence, and outcomes. Role-separated subagents run candidate skills on practice probes with redacted reporting and propose revisions informed by prior decisions, enabling cross-session refinement without rediscovering past rationale. We evaluate SkillHone on deep-research benchmarks in a raw open-web setting, where agents are not given an integrated search stack and must organize retrieval through portable skills. We compare against a deep-research agent backed by commercial retrieval services. With Qwen3.6-35B-A3B as the evaluation-time backbone, the resulting skills outperform the deep-research agent by 15.8 points on GAIA and 3.2 points on WebWalkerQA-EN, while also exceeding prior skill-evolution methods.

Motivated by the recency effect in online learning, we study algorithms for single-pass *sliding-window streaming multi-armed bandits (MABs)* in this paper. In this setting, we are given $n$ arms with unknown sub-Gaussian reward distributions and a parameter $W$. The arms arrive in a single-pass stream, and only the most recent $W$ arms are considered valid. The algorithm is required to perform pure exploration and regret minimization with limited memory, defined as the number of stored arms. The model is a natural extension of the streaming multi-armed bandits model (without the sliding window) that has been extensively studied in recent years. We provide a comprehensive analysis of both the pure exploration and regret minimization problems with the model. For pure exploration, we prove that finding the best arm is hard with sublinear memory while finding an approximate best arm admits an efficient algorithm. For regret minimization, we explore a new notion of regret and give sharp memory-regret trade-offs for any single-pass algorithm. We complement our theoretical results with experiments, demonstrating the trade-offs between sample, regret, and memory.

Offline reinforcement learning (RL) offers a path to policy improvement from logged data alone, using historical returns or other measurable outcomes as world feedback. A key difficulty is improving observed behavior without extrapolating beyond what the offline data supports. We propose \emph{counterfactual transport flows}, a source-conditioned trajectory refinement framework for offline decision-making guided by world feedback. Given a low-feedback candidate trajectory, we construct local preference pairs from offline data by retrieving nearby trajectories in latent trajectory space with higher task-specific feedback, and use them as weak supervision for conservative refinement. The framework learns instance-specific refinement directions: at inference time, a refinement strength parameter controls how far the candidate trajectory is transported, enabling a trade-off between preserving the original behavior and applying stronger improvement. Experiments on D4RL benchmarks, including AntMaze and MuJoCo tasks, show that our method improves behavior from historical returns as world feedback, while providing interpretable trajectory-level refinement paths.

Agentic reinforcement learning (RL) has become an important post-training paradigm for turning LLMs from static chatbots into interactive agents, giving rise to representative applications such as OpenClaw. Existing work mainly focuses on policy optimization algorithms and training frameworks, but pays less attention to the full data lifecycle of agent-environment interactions, from data production to training consumption. To bridge this gap, we present Claw-R1, an interactive step-level data middleware system for agentic RL. Claw-R1 connects heterogeneous agent runtimes with RL training backends through two core components: a Gateway Server and a Data Pool. The Gateway Server captures multi-turn interaction steps through a unified LLM API entry point, while the Data Pool organizes them into step-level records consisting of prompt IDs, response IDs, rewards and other metadata. In our demo, users can interactively inspect live trajectories, examine the state, action, and reward of each step, curate data by quality and readiness, and configure training-ready batches for different downstream RL algorithms. Overall, Claw-R1 treats agent interaction traces as managed data assets rather than temporary runtime logs. Through this demonstration, we hope to encourage the community to recognize the importance of data management in agentic RL. Our code is available at https://github.com/AgentR1/Claw-R1 and the demonstration video can be found at link https://youtu.be/Pw47dAOw6B0.

We prove that $ρ\text{-}\mathrm{NPTS}_{\mathrm{SG}}$, an anchor-free nonparametric Thompson Sampling algorithm for risk-averse bandits, achieves regret matching the instance-dependent lower bound to leading order in $\log n$, establishing it as asymptotically optimal for any continuous risk functional $ρ$ (CVaR, mean-variance, Sharpe ratio, distortion risk measures, and more) on the class of distributions with bounded density and sub-Gaussian tails, including Gaussian arms. Both this result and its bounded-support counterpart require only continuity of $ρ$: strictly weaker than the dominance condition of prior parametric Thompson Sampling results, and strictly weaker than the Lipschitz condition of UCB-type algorithms, yielding the first instance-optimal guarantees for non-Lipschitz functionals such as the Sharpe ratio without parametric reward assumptions. The bounded-support case is developed first as a stepping stone sharing the same proof structure. The key technical contributions are a discretisation lemma (bounded support) and a truncated discretisation lemma (sub-Gaussian tails), each projecting the growing-alphabet Dirichlet posterior onto a fixed grid via the Dirichlet aggregation property, holding all polynomial prefactors at fixed degree independent of sample size and breaking the super-exponential barrier that blocked prior proofs.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.

Contextual queueing bandits provide a framework for learning to schedule heterogeneous jobs under unknown context-dependent service rates. Under stochastic contexts, existing algorithms achieve $\widetilde{\mathcal{O}}(T^{-1/4})$ queue length regret, defined as the expected difference between the learner's and oracle's queue lengths at horizon $T$. In this paper, we improve this rate to $\widetilde{\mathcal{O}}(T^{-1/2})$. The key observation is that random exploration is needed only up to a carefully chosen cutoff round, rather than throughout the entire horizon. We propose CQB-$η$-2, a three-phase algorithm: (i) pure random exploration to construct an initial estimator, (ii) $η$-random exploration combined with a UCB rule to continue learning while maintaining negative drift, and (iii) pure UCB after the exploration cutoff. Our proof decomposes the queue length regret at the cutoff round. Before the cutoff, negative drift suppresses queue length differences caused by suboptimal choices. After the cutoff, the first two phases provide sufficient random exploration samples, ensuring that UCB decisions incur small departure-rate gaps. Combining these two bounds yields queue length regret of order $\widetilde{\mathcal{O}}(T^{-1/2})$. We further prove a minimax lower bound of order $Ω(T^{-1/2})$. The proof constructs two hard instances that are statistically indistinguishable up to the final service decision, and uses a queue-specific coupling argument to convert the resulting testing error into queue length regret. Together, our upper and lower bounds characterize the minimax dependence on the horizon $T$ up to logarithmic factors.

We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time. Under practitioner-friendly assumptions, we reduce this setting to linear bandit with stationary mean but heteroskedastic and non-stationary noise. We further study the case when the learner must ensure the mean reward of each decision must exceed that of a baseline strategy $\boldsymbolπ_0$ at each decision step. We introduce Dri-MED, an algorithm inspired from the linear version of the MED strategy, and carefully adapted to handle the non-stationary heteroskedastic noise. We show that the instance-dependent regret scales as $\tilde{\mathcal O}\left(\fracκ{\tildeΔ}d^2(\log(T)\right)$, where $\tildeΔ$ is the constraint-aware sub-optimality gap subject to policy $π_0$, with variance-aware multiplicative term $κ$ that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys $\tilde{\mathcal{O}}(d)$ expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.

Reinforcement learning (RL) has become a key component of post-training large language models (LLMs). In practice, LLM RL is often off-policy because of training-inference mismatch and policy staleness, making trust-region control essential for stable optimization. Mainstream methods such as PPO and GRPO approximate this control with a ratio-clipping mechanism, but the importance ratio can be a poor proxy for distributional shift in long-tailed vocabularies. Recent work such as DPPO addresses this mismatch by replacing ratio-based clipping with a divergence-based mask, yielding a trust region defined by the sampled token's absolute probability shift. However, DPPO still relies on a hard mask: once a token crosses the trust-region boundary in a harmful direction, its gradient is discarded rather than corrected. To address this, we propose Divergence Regularized Policy Optimization (DRPO), which replaces the hard mask with a smooth advantage-weighted quadratic regularizer on policy shift. DRPO preserves the same trust-region geometry as DPPO while inducing bounded, continuous gradient weights that attenuate diverging updates and provide corrective signals beyond the boundary. Experiments across model scales, architectures, and precision settings show that DRPO improves the stability and efficiency of LLM RL training.

Training reinforcement learning (RL) policies from scratch is costly: it requires careful reward and environment design, extensive tuning, and substantial computation. Yet many control problems already have a functional but suboptimal policy available as a baseline. This paper proposes a method for embedding such a baseline into the RL training process, simultaneously improving training efficiency relative to from-scratch methods and producing a learning policy that outperforms the baseline. At each step, the method arbitrates between the baseline policy and a trainable learning policy, initially relying strongly on the baseline policy and then progressively transferring agency to the learning policy. By the end of training, the learning policy is a standalone neural network that operates without baseline policy support. The paper formalizes what it means for the baseline policy to be functional: under this policy, the agent reaches a goal set and remains there with high probability. The proposed arbitration mechanism is designed to exploit this property during training, yielding high goal-reaching rates right from the beginning of training. A theoretical analysis provides a formal interpretation of this behavior under stated assumptions and extends it to the final baseline-free regime, where explicit lower bounds are derived for the goal-reaching probability of the standalone learning policy. Empirical results on continuous-control benchmarks show that the proposed method achieves returns that match or exceed those of competitive approaches, while maintaining the highest goal-reaching rates throughout training among the compared methods -- including in the final stage, where the learning policy operates without any baseline support.

We measure how well current large language models coordinate as multiple agents sharing a common resource, using the dining philosophers problem as a clean test bed. Across 630 episodes spanning seven models and three philosopher counts, four frontier closed-source systems reach mean reward 0.45 to 0.87 and Mistral-Small 24B reaches 0.83 to 0.99, while Qwen3-14B reaches 0.13 to 0.35. We then ask whether group relative policy optimization (GRPO) on rollouts from the task itself can close the gap and find that it cannot: a Welch's t-test on per-episode reward at five philosophers gives p = 0.66 and a Hedges' g of -0.11, with no statistically significant change at ten or fifteen philosophers either. Two further observations qualify the result. The training reward of both 8B and 14B runs peaked at step nine and then declined, so the default saved checkpoint at step 15 is strictly worse than several earlier ones. The four-term reward we use admits a degenerate maximum at zero actions, which DeepSeek-R1-Distill-Qwen-7B and Mistral-Small 24B at five philosophers both inhabit, with mean reward 1.0 and 0.83 respectively at zero meals. The bottleneck for an open-weight 14B model on multi-agent coordination is not training compute but training methodology: reward shaping that does not collapse to a no-action maximum, checkpoint discipline that does not depend on the final step, and curriculum across problem scales.

Reinforcement Learning from Human Feedback via Proximal Policy Optimization often suffers from policy mode collapse, brittle exploration loops, and distribution drift. This paper introduces Variational Proximal Policy Optimization (\(\textsc{VP}_2\textsc{O}\)), a particle-based variational inference framework that maps policy optimization to Stein Variational Gradient Descent within a Mixture-of-Experts architecture. By leveraging functional kernels over localized expert prototypes alongside an expert orthogonalization loss, \(\textsc{VP}_2\textsc{O}\) introduces a geometry-based proximal-control mechanism that can reduce reliance on fixed clipping or KL schedules. Our results on a 33B/4B sparse Mixture-of-Experts model show several improvements across complex reasoning benchmarks, establishing a \(+\mathbf{179}\) ELO gain on Codeforces and a \(\mathbf{32\%}\) reduction in token count on AIME mathematical reasoning tasks.

Reliable wildlife monitoring is essential for ecology and conservation, yet many existing methods, such as tagging, capture, and close-range observation, can alter the very behaviors they aim to measure. Aerial robots offer a scalable alternative, which has shown promising performance in multiple studies. Nonetheless, existing approaches typically lack behavioral awareness, rely on fixed heuristics, or require real-world training data that are costly, impractical, and ethically difficult to obtain. As a result, there remains no general framework for adaptive drone-based monitoring that can both preserve ecological validity and scale across species, behaviors, and robotic platforms. In this study, we introduce a disturbance-aware reinforcement-learning-based framework for heterogeneous aerial robotic fleets that enables autonomous wildlife tracking while explicitly minimizing behavioral disruption. We couple a zoologically grounded simulation environment with fitted animal movement models derived from real trajectory statistics, and train control policies using a reward formulation that captures the trade-off between observation quality and disturbance risk. Across three species (pigeon, jackal, and spur-winged lapwing) with distinct ecologies and motion patterns and four increasingly strategic behavior models common in nature, the learned policies consistently surpassed currently used rule-based baselines and generalized across monitoring tasks, animal dynamics, and drone types. These results establish disturbance-aware learning as a viable foundation for non-invasive autonomous wildlife observation, opening a path towards scalable, ethically responsible, and scientifically reliable robotic monitoring in ecology and conservation.

Enabling humanoid robots to operate in complex, dynamic environments remains a critical challenge, fundamentally limited by the ability to navigate robustly, safely, and accurately. While reinforcement learning with velocity-commanded policies has achieved remarkable robustness in humanoid locomotion, this approach lacks explicit control of the foothold placement, leading to unsafe behavior, such as stepping onto human feet, or imprecise navigation, hindering the following manipulation task. Conversely, explicit foothold-tracking policies offer a promising alternative by directly being commanded with target foot poses. However, existing approaches are often limited by unrealistic state assumptions, compromising real-world deployment, or they are part of staged pipelines, making them tied to specific downstream tasks. In this work, we introduce a novel, lightweight framework for training general-purpose 3D foothold-tracking policies. By dynamically providing footstep support through a goal sampler, this method enables the learned policy to be agnostic to specific terrains. Our new target representation effectively mitigates challenges arising in the real world, such as noisy and inaccurate pose estimation and foot contact estimation. Designed for direct real-world transfer, our policy acts as a standalone low-level controller that can be seamlessly paired with various high-level foothold generators. We demonstrate the effectiveness of our framework through extensive experiments in simulation and in the real world. By coupling our policy with different upstream planners, we achieve natural and accurate locomotion in challenging settings, paving the way for loco-manipulation tasks in complex environments.

Quantum reinforcement learning (QRL) is a promising approach to learn effective decision strategies across several applications with stochastic environments. Instead of directly modeling the random variables that govern these environments, existing QRL architectures indirectly approximate environment behavior by estimating expected outcomes, which limits their expressive power and adaptive potential. Overcoming such challenges requires a novel QRL approach that exploits the distributional nature of quantum computers to directly model environment random variables as quantum state distributions. Hence, in this paper, a novel framework dubbed quantum-native reinforcement learning (QnRL) is proposed. QnRL is a distributional RL framework that learns conditional distributions naturally in Hilbert space via superimposed and entangled quantum states. Thus, QnRL can directly model the behavior of stochastic learning environments via the natural properties of quantum systems. QnRL accomplishes this via a novel, proposed quantum amplitude kickback (QuAK) algorithm that enables comparing the $n$-th power of the $m$-th moment of multiple superimposed distributions. It is theoretically proven that a conditional action policy distribution is distilled from the moments of a quantum generative model entirely within Hilbert space via QuAK, and optimized via QnRL. This complex distribution composition is also shown to provide extra dimensions for expressing environment correlations that are unknown to purely classical and classically-sampled quantum distributional models. Experimental results across diverse environments show that QnRL achieves up to $82.9\%$ higher evaluation scores, with up to $94.3\%$ fewer parameters on average, more accurately estimates the expected return for unseen observations, and better adapts to varying stochastic conditions compared to the baseline.

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving the reasoning capabilities of large language models (LLMs). Recent tree-based methods such as TreeRPO extend flat trajectory sampling with tree-structured rollouts to obtain dense, step-level reward signals without a separate process reward model. However, not all trees are equally informative: trees where all leaves succeed, all leaves fail, or the policy already predicts the reward distribution contribute little to gradient updates, wasting compute. We introduce CATPO (Critique-Augmented Tree Policy Optimization), which diagnoses and addresses this waste at the tree level. CATPO first scores each tree via a tree informativeness score, F(T), combining leaf-outcome diversity with policy-reward decorrelation at zero extra compute. For dead-wrong trees where all branches fail, CATPO applies critique-guided healing: it locates the shallowest failure point, generates a natural-language critique, and grafts refined continuations to recover training signal. Finally, an informativeness-weighted loss scales each tree's gradient contribution by its normalized score, concentrating parameter updates on the most informative trees while preserving overall gradient magnitude. Experiments on Qwen2.5-Math-1.5B trained with the MATH dataset show that CATPO achieves 37.5% macro accuracy across four benchmarks (AIME24, MATH-500, OlympiadBench, and MinervaMath), improving over TreeRPO by 1.9% and GRPO by 4.8%.

This study addresses the optimal execution of large stock sell programs by introducing TT-DAC-PS (Twin-Target Deterministic Actor-Critic with Policy Smoothing), a deterministic actor-critic architecture that combines twin exponential-moving-average critic targets with pessimistic min backup, TD3-style target policy smoothing noise, delayed actor updates, and conservative Q regularisation to curb overestimation. Exploration uses Ornstein-Uhlenbeck (OU) noise with a hybrid schedule: deterministic episode-wise decay, variance-guided adjustment based on recent reward dispersion, and a Soft Actor-Critic (SAC)-style temperature that is learned and mapped to the noise scale. The environment integrates Almgren-Chriss (AC) trade impact with Limit Order Book (LOB) prices and volumes, normalised state features, per-step volume participation caps, and a utility-based reward. The trade execution algorithm is applied to LOB data for ten U.S. stocks. Performance is assessed against reinforcement-learning baseline algorithms, including Proximal Policy Optimisation (PPO), Soft Actor-Critic (SAC), and Advantage Actor-Critic (A2C), as well as alternative trade execution algorithms, including Time-Weighted Average Price (TWAP), Volume-Weighted Average Price (VWAP), and AC. The proposed model consistently reduces mean implementation shortfall percentage with competitive variance, outperforming classical baselines and standard reinforcement-learning benchmark models.

Autonomous Underwater Vehicles (AUVs) traditionally rely on complex, heavily engineered pipelines for perception, path planning, and motion control. This paper explores the feasibility of an end-to-end Deep Reinforcement Learning (DRL) approach that maps raw sensor data directly to thruster commands, reducing manual engineering. We propose a hierarchical reinforcement learning (HRL) architecture splitting the problem into two Markov Decision Processes. A High-Level (HL) policy operating at 2Hz processes raw $84 \times 84$ pixel monocular camera frames, stacked $100 \times 100$ pixel forward-looking imaging sonar, and proprioceptive data to generate spatial subgoals. Simultaneously, a Low-Level (LL) policy operating at 10Hz converts these subgoals into thruster commands. The HL policy is trained using Reinforcement Learning from Prior Demonstrations (RLPD) within a modified Sample-Efficient Robotic Reinforcement Learning (SERL) framework, while the LL policy utilizes Soft Actor-Critic (SAC) combined with Hindsight Experience Replay (HER). Evaluated in the high-fidelity HoloOcean simulator, our method demonstrates successful obstacle avoidance, achieving trajectory lengths closely approximating (within 4% to 6% of) an $\text{RRT}^*$ planning baseline. Furthermore, the learned policy exhibits strong robustness to simulated sensor noise and decreased visibility. While the system navigates familiar geometries effectively, experiments reveal generalization limitations when encountering unvisited areas with novel obstacle shapes. Ultimately, this work demonstrates the promise of sample-efficient, end-to-end DRL for underwater navigation using minimal computational hardware.

We study a stochastic multi-armed bandit problem in which the set of available arms expands over time. This setting arises in sequential experimentation when new actions or treatments become available during an ongoing study, making regret against a single best arm in hindsight inappropriate. We instead evaluate performance relative to the best arm currently available, leading to a dynamic-regret criterion for arriving-arm environments. To address the resulting challenges of arrival information discrepancy (AID) and a drifting benchmark (DB), we propose UCB for Arriving Arms (UCB-AA), an elimination-based procedure with an aiding preliminary screening step for newly arrived arms before full competition with incumbent arms. We show that UCB-AA attains regret bounds that depend explicitly on the arrival process, achieves sublinear dynamic regret under regularity conditions on gap evolution, and admits an online extension for unknown horizons. Simulation results show that UCB-AA reduces wasted pulls and maintains a smaller active arm set while preserving competitive regret performance.

The transformation towards renewable energy and feedstock supply in the chemical industry requires new conceptual process design approaches. Recently, breakthroughs in artificial intelligence offer opportunities to accelerate this transition. Specifically, deep reinforcement learning, a subclass of machine learning, has shown the potential to solve complex decision-making problems and aid sustainable process design. We survey state-of-the-art research in reinforcement learning for process design through three major elements: (i) information representation, (ii) agent architecture, and (iii) environment and reward. Moreover, we discuss perspectives on underlying challenges and promising future works to unfold the full potential of reinforcement learning for process design in chemical engineering.

Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we study two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) that disqualifies priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS) that utilizes a bi-level Thompson sampling scheme. We theoretically analyze the algorithms and establish a sublinear regret bound for HP-GP-TS. In addition, we demonstrate the effectiveness of these algorithms compared to the alternatives through extensive experiments with synthetic and real-world data.

Interactively learning from observation and language feedback is an increasingly studied area driven by the emergence of large language model (LLM) agents. Despite impressive empirical demonstrations, so far a principled framing of these decision problems remains lacking. We formalize the Learning from Language Feedback (LLF) problem, assert sufficient assumptions to enable learning despite latent rewards, and introduce $\textit{transfer eluder dimension}$ as a measure to characterize the hardness of LLF. We formalize the intuition that information in the language feedback governs the learning complexity, and demonstrate cases where learning from rich language feedback can be exponentially faster than learning from reward. We develop a no-regret algorithm, called $\texttt{HELiX}$, that provably solves LLF problems through sequential interactions, with performance guarantees that scale with the transfer eluder dimension. Across several empirical domains, we show that $\texttt{HELiX}$ performs well even when repeatedly prompting LLMs does not work reliably. Our contributions mark an important step towards designing principled interactive learning algorithms using generic language feedback.

We introduce Unsupervised Partner Design (UPD), a population-free multi-agent reinforcement learning method for robust ad-hoc teamwork. UPD generates training partners on-the-fly and selects them adaptively based on a learnability criterion, removing the need for pre-trained partner populations or manual parameter tuning. We show that this simple mechanism enables effective partner diversity and can be extended to joint partner-environment selection when a procedural level generator is available. Across Level-Based Foraging, Overcooked-AI, and the Overcooked Generalisation Challenge, UPD consistently achieves strong performance compared to both population-based and population-free baselines. In a human-AI user study, agents trained with UPD achieve higher returns and are rated as more adaptive, more human-like, and less frustrating than all evaluated baseline methods.

Reinforcement learning (RL) agents often struggle to generalize to new tasks and contexts without updating their parameters, mainly because their learned representations and policies are overfit to the specifics of their training environments. To boost agents' in-context RL (ICRL) ability, this work formulates ICRL as a two-agent emergent communication problem and introduces CORAL (Communicative Representation for Adaptive RL), a framework that learns a transferable communicative context by functionally separating latent representation learning from control. In CORAL, an Information Agent (IA) is pre-trained as a world model on a diverse distribution of tasks. Its objective is not direct return maximization, but world modeling and distilling its understanding into concise messages. The emergent communication protocol is shaped by a novel Causal Influence Loss, which measures the effect that the message has on the next action. During deployment, the previously trained IA serves as a fixed contextualizer for a new Control Agent (CA), which learns to solve tasks by interpreting the provided communicative context. Our experiments demonstrate that this approach enables the CA to achieve significant gains in sample efficiency and successfully perform zero-shot adaptation with the help of pre-trained IA in diverse online and offline environments, validating the efficacy of learning a transferable communicative representation.

We present BLINQ, a new model-based algorithm that learns the Whittle indices of an indexable, communicating and unichain Markov Decision Process (MDP). Our approach relies on building an empirical estimate of the MDP and then computing its Whittle indices using an extended version of a state-of-the-art existing algorithm. We provide a proof of convergence to the Whittle indices we want to learn as well as a bound on the time needed to learn them with arbitrary precision. Moreover, we investigate its computational complexity. Our numerical experiments suggest that BLINQ significantly outperforms existing Q-learning approaches in terms of the number of samples needed to get an accurate approximation. In addition, it has a total computational cost even lower than Q-learning for any reasonably high number of samples. These observations persist even when the Q-learning algorithms are speeded up using neural networks to predict Q-values.

Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs. Within this framework, we develop a preference-based adversarial attack to generate hard instances that expose solver weaknesses, and quantify the attack impact by the resulting degradation on Pareto-front quality. We further introduce a defense strategy that integrates hardness-aware preference selection into adversarial training to reduce overfitting to restricted preference regions and improve out-of-distribution performance. The experimental results on multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) verify that our attack method successfully learns hard instances for different solvers. Furthermore, our defense method significantly strengthens the robustness and generalizability of neural solvers, delivering superior performance on hard or out-of-distribution instances.

Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has reduced the number of training steps required to reach peak performance, the overall wall-clock training time often remains unchanged or even increases due to higher per-step cost. We propose MMR-GRPO, which integrates Maximal Marginal Relevance to reweigh rewards based on completion diversity. Our key insight is that semantically redundant completions contribute limited marginal learning signal; prioritizing diverse solutions yields more informative updates and accelerates convergence. Extensive evaluations across three model sizes (1.5B, 7B, 8B), three GRPO variants, and five mathematical reasoning benchmarks show that MMR-GRPO achieves comparable peak performance while requiring on average 47.9% fewer training steps and 70.2% less wall-clock time. These gains are consistent across models, methods, and benchmarks. Our code is released at: https://github.com/WeiKangda/MMR-GRPO.

While Large Language Model (LLM) agents excel at general tasks, they inherently struggle with continual adaptation due to the frozen weights after deployment. Conventional reinforcement learning (RL) offers a solution but incurs prohibitive computational costs and the risk of catastrophic forgetting. We introduce Just-In-Time Reinforcement Learning (JitRL), a training-free framework that enables test-time policy optimization without any gradient updates. JitRL maintains a dynamic, non-parametric memory of experiences and retrieves relevant trajectories to estimate action advantages on-the-fly. These estimates are then used to directly modulate the LLM's output logits. We theoretically prove that this additive update rule is the exact closed-form solution to the KL-constrained policy optimization objective. Extensive experiments on WebArena and Jericho demonstrate that JitRL establishes a new state-of-the-art among training-free methods. Crucially, JitRL outperforms the performance of computationally expensive fine-tuning methods (e.g., WebRL) while reducing monetary costs by over 30 times, offering a scalable path for continual learning agents. The code is available at https://github.com/liushiliushi/JitRL.

Reinforcement learning (RL) with combinatorial action spaces remains challenging because feasible action sets are exponentially large and governed by complex feasibility constraints, making direct policy parameterization impractical. Existing approaches embed task-specific value functions into constrained optimization programs or learn deterministic structured policies, sacrificing generality and policy expressiveness. We propose a solver-induced \emph{latent spherical flow policy} that brings the expressiveness of modern generative policies to combinatorial RL while guaranteeing feasibility by design. Our method, LSFlow, learns a \emph{stochastic} policy in a compact continuous latent space via spherical flow matching, and delegates feasibility to a combinatorial optimization solver that maps each latent sample to a valid structured action. To improve efficiency, we train the value network directly in the latent space, avoiding repeated solver calls during policy optimization. To address the piecewise-constant and discontinuous value landscape induced by solver-based action selection, we introduce a smoothed Bellman operator that yields stable, well-defined learning targets. Empirically, our approach outperforms state-of-the-art baselines by an average of 20.6\% across a range of challenging combinatorial RL tasks.

Existing alignment methods directly use the reward model learned from user preference data to optimize an LLM policy, subject to KL regularization with respect to the base policy. This practice is suboptimal for maximizing user's utility because the KL regularization may cause the LLM to inherit the bias in the base policy that conflicts with user preferences. While amplifying rewards for preferred outputs can mitigate this bias, it also increases the risk of reward hacking. This tradeoff motivates the problem of optimally designing reward models under KL regularization. We formalize this reward model optimization problem as a Stackelberg game, and show that a simple reward shaping scheme can effectively approximate the optimal reward model. We empirically evaluate our method in inference-time alignment settings and demonstrate that it integrates seamlessly into existing alignment methods with minimal overhead. Our method consistently improves average reward and achieves win-tie rates exceeding 66% against all baselines, averaged across evaluation settings.

We study offline reinforcement learning under $Q^\star$-approximation and partial coverage, a setting that motivates practical algorithms such as Conservative $Q$-Learning (CQL; Kumar et al., 2020) but has received limited theoretical attention. Our work is inspired by the following open question: "Are $Q^\star$-realizability and Bellman completeness sufficient for sample-efficient offline RL under partial coverage?" We answer in the negative via an information-theoretic lower bound. To identify additional structure that enables sample-efficient offline RL under partial coverage, we introduce a general decision-estimation framework, inspired by model-free decision-estimation coefficients (DEC) for online RL (Foster et al., 2023b; Liu et al., 2025b). Our framework decomposes offline RL complexity into decision complexity and value estimation error. This allows modular study of both sub-problems. Our result not only unifies existing results (Chen and Jiang, 2022; Uehara et al., 2023), but further improves and generalizes them. On the decision complexity side, our improvement includes: the first $ε^{-2}$ sample complexity bound for soft $Q$-learning under partial coverage that improves Uehara et al.'s (2023) $ε^{-4}$ bound, the removal of the need for additional online interaction in the value-gap setting of Chen and Jiang (2022), and new learnable settings beyond the above two cases. On the value estimation side, we provide a new characterization of the role of Bellman completeness under partial coverage, and the first characterization of offline learnability for general low-Bellman-rank MDPs (Jiang et al., 2017; Du et al., 2021; Jin et al., 2021). The latter is a canonical online RL setting that has remained unexplored in offline RL except for special cases. As a side contribution, our techniques give the first analysis of CQL in the function approximation setting.

Reinforcement learning (RL) has become essential for post-training large language models (LLMs) in reasoning tasks. While scaling rollouts can stabilize training and enhance performance, the computational overhead is a critical issue. In algorithms like GRPO, multiple rollouts per prompt incur prohibitive costs, as a large portion of prompts provide negligible gradients and are thus of low utility. To address this problem, we investigate how to select high-utility prompts before the rollout phase. Our experimental analysis reveals that sample utility is non-uniform and evolving: the strongest learning signals concentrate at the ``learning edge", the intersection of intermediate difficulty and high uncertainty, which shifts as training proceeds. Motivated by this, we propose HIVE (History-Informed and online-VErified prompt selection), a dual-stage framework for data-efficient RL. HIVE utilizes historical reward trajectories for coarse selection and employs prompt entropy as a real-time proxy to prune instances with stale utility. By evaluating HIVE across multiple math reasoning benchmarks and models, we show that HIVE yields significant rollout efficiency without compromising performance.

Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where the population distribution evolves stochastically. This stochasticity compels agents to adopt population-aware policies to respond to aggregate shocks. We formulate two distinct learning objectives: recovering a Nash equilibrium and maximizing performance against an expert population. We investigate two imitation proxies: Behavioral Cloning (BC) and Adversarial (ADV) divergence. We then establish finite-sample error bounds showing that minimizing these proxies effectively controls both the policy's exploitability and its performance gap relative to the expert. Furthermore, we propose a numerical framework using generalized Fictitious Play and Deep Learning to compute expert population-aware policies. Through experiments on three environments we demonstrate that standard population-unaware policies fail to capture the equilibrium dynamics. Our results highlight that learning population-aware policies is crucial to avoid being misled by the randomness inherent in common noise.

Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions. For the entropy-regularized RL objective, WPG evolves each state-conditional policy by transporting it along the action gradient of the soft Q-function together with a Langevin-type diffusion. Despite its appeal for continuous-control problems, its global convergence properties remain poorly understood. Standard Langevin analyses do not directly apply, because the RL objective depends on the policy through the Bellman recursion rather than through a static convex functional, and the Langevin drift is determined by the soft Q-function, whose regularity must be controlled along the policy iterates. In this paper, we develop a global convergence theory for WPG by exploiting the Bellman structure of entropy-regularized RL. We show that the role usually played by convexity can be replaced by a Bellman-based argument: the soft Bellman residual admits a statewise KL representation with respect to a Gibbs policy; Bellman contraction relates this residual to the global optimality gap; and a Bellman resolvent identity connects value improvement to relative Fisher information. Combined with a uniform log-Sobolev inequality (LSI) for the evolving Gibbs family, these ingredients yield a distributional Polyak--Łojasiewicz condition. We further establish the regularity and uniform bounds needed to control the discretization error, thereby obtaining geometric contraction up to a discretization bias. Conceptually, our analysis shows that although entropy-regularized RL is not convex in the usual flat sense, the Bellman recursion induces a favorable Polyak--Lojasiewicz-type (PL) geometry that supports global convergence of WPG.

Multi-omics data provide complementary molecular characterizations of disease phenotypes and play an important role in disease diagnosis and subtype classification in precision medicine. However, acquiring complete multi-omics profiles is expensive and time-consuming, while most existing deep learning methods assume full modality availability during inference, resulting in substantial redundancy and limited practicality in clinical settings. To address this issue, we propose SDM-Q, a reinforcement learning framework for adaptive and cost-aware multi-omics classification. Specifically, multi-omics diagnosis is reformulated as a finite-horizon sequential decision problem, where the currently acquired omics modalities define the diagnostic state at each stage. An action--value function determines whether to acquire an additional modality or terminate the decision process and output the final prediction. To balance diagnostic utility and acquisition cost, the reward is defined only at the terminal stage and jointly determined by classification correctness and cumulative modality acquisition cost. A backward stage-wise optimization strategy is introduced to improve policy consistency and training stability. Experiments on four public multi-omics datasets, including ROSMAP, LGG, BRCA, and KIPAN, demonstrate that SDM-Q effectively reduces redundant modality acquisition while maintaining competitive classification performance compared with methods using complete multi-omics inputs. In the BRCA and KIPAN datasets, more than 99\% and 95\% of subjects, respectively, achieve accurate classification using only a single omics modality, while the average number of acquired modalities remains below two for ROSMAP and LGG. These results suggest that cost-aware sequential decision-making provides an effective paradigm for improving the efficiency of precision medicine workflows.

Reinforcement Learning (RL) has received increasing attention and adoption in real-world use cases. Most of these systems follow a train-then-fix paradigm, where trained agents do not learn while interacting with the world until performance degrades and retraining becomes necessary. In this position paper, we argue that deploying an agent that is incapable of optimality, but receives an evaluative reward signal, is inherently a continual RL problem. We identify four sources of non-stationarity after deployment that necessitate never-ending learning, and highlight why the best deployed agents never stop adapting. We analyze successful examples of continual RL in the real world, and present the community with the advantages and measures to move away from the current train-then-fix paradigm.

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Intelligent tutoring systems increasingly rely on reinforcement learning to personalise instruction, yet optimising for observable engagement signals can systematically decouple learner activity from genuine knowledge acquisition. Analysing over 21 million student interactions across two deployed platforms, we find engagement events without corresponding mastery gains occur in 26.5% of interactions on Junyi Academy (72,758 students) and 3.1% on XES3G5M (14,453 students, NeurIPS 2023), confirming this pattern is directly observable in deployed educational technology at scale. We introduce Mastery-Conditioned Constrained Policy Optimisation (MC-CPO), a reinforcement learning framework that addresses this problem structurally. MC-CPO conditions the admissible instructional action space on learner mastery state: a concept becomes available only when prerequisite knowledge meets a mastery threshold, yielding an action space that expands naturally as learners acquire knowledge. Pedagogical safety constraints are enforced by construction, with formal guarantees of structural prerequisite safety, primal-dual convergence, and strict dominance over post-hoc filtering. MC-CPO is the only method to reduce reward hacking severity across all conditions. Mean per-episode mastery gain increases by 18.3% on Junyi Academy and 54.0% on XES3G5M relative to all baselines, while competitive engagement performance is maintained. These results support structural constraint modelling as a principled foundation for safer adaptive instructional policies in deployed tutoring systems.

Long-horizon embodied tasks remain a fundamental challenge in AI, as current methods rely on hand-engineered rewards or action-labeled demonstrations, neither of which scales. We introduce ASH, an agentic system that learns an embodied policy from unlabeled, noisy internet video, without reward shaping or expert annotation. ASH follows a self-improvement loop; when it gets stuck, ASH learns an Inverse Dynamics Model (IDM) from its own trajectories, and uses its IDM to extract supervision from relevant internet video. ASH uses unsupervised learning to identify key moments from large-scale internet video and retains them as long-term memory -- allowing it to tackle long-horizon problems. We evaluate ASH on two complementary environments demanding multi-hour planning: Pokemon Emerald, a turn-based RPG, and The Legend of Zelda: The Minish Cap, a real-time action-adventure game. In both games, behavioral cloning, retrieval-augmented and zero-shot foundation-model baselines plateau, while ASH sustains progression across our 8-hour evaluation. ASH reaches an average of $11.2/12$ milestones in Pokemon Emerald and $9.9/12$ in Legend of Zelda, while the strongest baseline gets stuck in both environments at an average of $6.5/12$ and $6.0/12$ milestones, respectively. We demonstrate that self-improving agents are a scalable recipe for long-horizon embodied learning.

Before an LLM agent can use a tool, a retrieval system must decide which candidate tools to show to the agent. How long should that shortlist be? Show too many tools and the model struggles to choose. Show too few and the correct tool may not appear. Most systems apply a fixed shortlist size to every query, but no standard metric exists to evaluate whether that size was appropriate. We treat the number of tools shown to an LLM agent as the object of evaluation and we apply Bits-over-Random (BoR), a chance-corrected metric that asks whether success at a given depth is better than what random selection would achieve at that same depth. We evaluate BoR across three tool-selection benchmarks, multiple scorers, and registries ranging from 20 to 3,251 tools. We then turn the same principle into a reinforcement learning (RL) reward for choosing tool shortlist depth per query. The RL agent is deliberately simple, serving as a probe of the metric rather than a proposed system. As the shortlist grows, random chance of including the correct tool rises, so the reward naturally decreases, reducing the need for an engineered depth penalty. On BFCL (370 tools), the learned policy nearly matches the coverage of showing 50 tools ($90.3\%$ vs $90.8\%$) while presenting only 7 on average. On ToolBench (3,251 tools), a fixed shortlist of 5 tools achieves higher aggregate coverage ($64.7\%$ vs $61.9\%$) but finds nothing on hard queries (correct tool ranked 6th-20th). The BoR agent finds $16.7\%$ on those same queries by searching deeper. Downstream validation with Claude Sonnet 4.6 indicates that shorter adaptive lists also improve the LLM's ability to select the right tool: $93.1\%$ versus $87.1\%$ when always shown 5 tools, widening to $76.8\%$ vs $60.9\%$ on medium-difficulty queries where the correct tool is present but not ranked first.

Reinforcement learning with verifiable rewards (RLVR) has driven breakthroughs in domains such as math, tool-use, and software engineering, yet its extension to computer-use agents (CUAs) has been bottlenecked by the scarcity of scalable training data with deterministic rewards. Constructing such data for CUAs requires consistent task instruction, executable environment, and verifiable reward. However, hand-curated benchmarks achieve high reward fidelity but cover few applications and LLM-as-judge-based datasets scale broadly but lack reliable verification. We present CUA-Gym, a scalable pipeline that co-generates task instructions, environment states, and reward functions. Concretely, a Generator agent constructs the initial and golden environment states, and a separate Discriminator agent writes the reward function from the task specification. An orchestrator agent drives the two through iterative rounds upon execution. Generated tuples then pass a final filter combining LLM majority voting and agent rollouts, ensuring quality beyond the per-task adversarial loop. To address the scarcity of training environments, we further synthesize CUA-Gym-Hub, a broad suite of high-fidelity mock web applications grounded in real-world software-use distributions, expanding the scale of CUA RLVR data by magnitude. Using this pipeline, we construct CUA-Gym, a dataset of 32,112 verified RLVR training tuples grounded in 110 environments. Trained with GSPO on CUA-Gym, our CUA-Gym-A3B and CUA-Gym-A17B achieve 62.1% and 72.6% on OSWorld-Verified, outperforming prior open-source CUAs at comparable scales, with performance scaling smoothly in both data volume and environment diversity. The same checkpoints also improve on the held-out WebArena benchmark, indicating transfer beyond the training environments. We will open-source the full synthesis pipeline, dataset, CUA-Gym-Hub environments, and models.

Safe reinforcement learning (RL) for robotic systems requires policies that improve task performance while satisfying state and input constraints during both training and deployment. Control barrier functions (CBFs) provide a principled mechanism for enforcing forward invariance through minimally invasive safety filters, but their use in model-free RL is limited by the need for accurate dynamics and hand-designed barrier certificates. We propose Robust Koopman-CBF SAC, a safety-filtered actor--critic framework that learns a finite-dimensional Koopman predictor from data, constructs affine CBF constraints in the lifted space, and enforces them through a quadratic-program safety layer. To account for finite-dimensional Koopman approximation error, the CBF condition is tightened using a projected residual margin estimated from held-out rollout data. The critic is trained on the executed safe action, while the actor is regularized toward the Koopman-CBF feasible set, reducing dependence on the filter over training. Across safe-control benchmarks, the method achieves zero constraint violations on CartPole stabilization and tracking while matching or exceeding unconstrained SAC returns. On high-dimensional Safety Gymnasium locomotion tasks, the method reduces violations in some settings but also exposes important limitations of first-order velocity barriers and linear EDMD models, motivating high-order and multi-step Koopman-CBF extensions. These results suggest that robust Koopman-CBF filters are a promising bridge between model-free RL and certifiable safety, while clarifying the structural conditions under which such filters remain effective.

Agentic reinforcement learning (RL) enables LLM agents to improve continuously from environment rewards, yet the resulting policies do not systematically accumulate reusable strategies that generalize across tasks. Modular skills can provide such reusable strategies, yet existing skill-augmented RL methods decouple skill creation from policy optimization, risking adopting skills that conflict with the evolving policy. Inspired by Anthropic's Skill Creator, we introduce ReSkill, an RL-in-the-loop skill creation framework that reconciles skill evolution with policy learning. ReSkill exploits the group-wise structure of GRPO to naturally embed three mechanisms with only marginal additional overhead: (1) an assertion-driven skill creator that diagnoses failures from past experience and proposes conditional, trigger-based skill revisions; (2) within-group rollout sampling that enables controlled comparison of skill versions, capturing which version best supports the policy's ongoing learning; and (3) Thompson Sampling with adaptive discounting to balance exploration and exploitation in skill version selection as the policy evolves. Across several domains, ReSkill consistently outperforms existing memory and skill-based RL methods, with the largest gains on unseen tasks. Analysis of the skill lifecycle shows skills being automatically created, tested, refined, and pruned as the policy improves, demonstrating reconciled skill-policy co-evolution.

Many current agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure: when an outcome diverges from prediction, the why and when of the mismatch are not systematically logged, reviewed, or corrected, so the same error can recur episode after episode. We argue that this is a structural problem, not merely a model-capacity one. We propose long-horizon temporal regret as a first-class objective alongside outcome regret and epistemic regret over the working causal model. Temporal regret captures when failure persists: how long a miscalibrated causal model is tolerated before correction. Epistemic regret captures why failure persists: residual uncertainty or error in the working causal model. Together, the three regrets give a falsifiable account of what, why, and when a long-lived agent can fail. Modeling the agent as a stream of E episodes, we prove three conditional results under explicit causal-probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot distinguish causal from spurious structure without an intervention channel, so temporal miscalibration can persist linearly even after outcome regret is driven to zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in the episode horizon, inducing O(log E) temporal regret. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and pre-register five falsifiable predictions. On CausalBench-Seq, Trivium follows the predicted logarithmic envelope while outcome-only baselines grow linearly. A pilot real-LLM stream provides preliminary external-validity evidence across one full E = 500 run and three E = 100 frontier-model pilots. Self-learning here means revising an external causal model, not retraining LLM weights.

Thompson sampling has proven effective across a wide range of stationary bandit environments. However, as we demonstrate in this paper, it can perform poorly when applied to non-stationary environments. We show that such failures are attributed to the fact that, when exploring, the algorithm does not differentiate actions based on how quickly the information acquired loses its usefulness due to nonstationarity. Building upon this insight, we propose predictive sampling, an algorithm that deprioritizes acquiring information that quickly loses usefulness. Theoretical guarantee on the performance of predictive sampling is established through a Bayesian regret bound. We provide versions of predictive sampling for which computations tractably scale to complex bandit environments of practical interest. Through numerical simulations, we demonstrate that predictive sampling outperforms Thompson sampling in all non-stationary environments examined.

Accurate carbon emission monitoring is critical for climate policy and emerging regulatory mechanisms such as the EU Carbon Border Adjustment Mechanism, yet city-level high-frequency monitoring data remain extremely scarce, severely limiting data-hungry deep learning models. Time series generation is a natural remedy, but existing GAN and diffusion-based generators often provide limited explicit supervision for the domain structure of carbon emission data: they may match marginal distributional statistics while insufficiently preserving cross-variable correlations between CO$_2$ and co-emitted pollutants and meteorological factors, and tend to collapse the first-difference statistics of atmospheric measurements, producing sequences that are smooth on average but lack the realistic step-wise variability of the underlying signals. We propose TriHead-GAN, a Transformer-based adversarial framework whose triple-head discriminator jointly supervises three complementary aspects of the joint distribution: distributional authenticity via a Wasserstein critic, cross-variable dependency via leakage-free regression of the target variable, and step-wise temporal smoothness via adjacent-difference prediction. The generator combines global self-attention with local temporal convolution, per-step noise injection, and an anti-smoothing loss that matches first-difference statistics. Experiments on the self-collected Changsha Carbon dataset, two public carbon datasets (China, US), and the ETTh1 benchmark show that TriHead-GAN achieves favorable performance over mainstream baselines on the vast majority of settings, and that the resulting synthetic windows improve downstream forecasting accuracy in low-resource carbon monitoring scenarios.

Ordinal Regression (OR) aims to predict target values with inherent order, underpinning critical applications across diverse domains, from recommender systems to computer vision. Though having evolved from naive regression to discretization-based classification and generation, existing paradigms remain fundamentally constrained by quantization artifacts and the lack of global ordinal topological perception. These methods typically enforce rigid boundary delineations, failing to capture the non-stationary semantic transitions inherent to ordinal data. In this paper, we propose a novel paradigm where OR is formulated as a Continuous Generative Ordinal Regression task. Under the novel paradigm, we introduce DiffOR, a unified framework that leverages diffusion models to recover continuous ordinal values via iterative denoising, thereby enabling the dynamic learning of soft semantic transitions. To explicitly preserve ordinal topology, we devise a Dual-Decoupling Strategy: Spatially, Multi-scale Increment Aggregation decomposes targets into hierarchical continuous increments; Temporally, Dynamic Denoising Perception synchronizes denoising steps with feature frequencies, ensuring robust coarse-to-fine refinement. Theoretically, we show that the proposed method can significantly enhance both representation capability and mechanistic interpretability. Extensive experiments on 12 benchmarks across four domains validate DiffOR's consistent superiority over state-of-the-art methods, establishing a new standard that demonstrates strong potential as a general-purpose solution for universal ordinal regression.

Understanding cellular phenotypes and how they respond to perturbations is critical for disease biology and therapeutic design. Single-cell RNA sequencing enables characterization at cellular resolution, yet the combinatorial space of conditions makes exhaustive experimental mapping infeasible. We introduce single-cell Concept Bottleneck Generative Models (scCBGM), a framework for interpretable and precise counterfactual editing of individual cells. scCBGM adapts concept bottleneck architectures for single-cell data through decoder skip connections and a cross-covariance penalty that promotes disentanglement without dimensional constraints. We extend the framework to flow matching models, enabling concept-guided editing in both encoding-decoding and generation regimes. To enable rigorous evaluation, we develop a synthetic benchmark with ground-truth counterfactuals. Across multiple real datasets, scCBGM demonstrates superior performance in combinatorial generalization and counterfactual prediction, supported by cell-level validation on synthetic data and population-level benchmarks on real datasets.

A fundamental tension exists in the large-step inference of diffusion models via their deterministic probability flow ordinary differential equation (PF-ODE) trajectories, which we identify as the contractivity trap: efficient inference favors large step sizes, while aggressive steps and highly expressive denoisers can undermine contraction-based stability certificates for error suppression. To address this, we propose SteinDiff, a step-wise inference-time stabilization framework that employs Stein-derived corrections without requiring reference samples. Specifically, SteinDiff introduces a geometry-aware residual correction mechanism that regularizes large-step solver updates without retraining. To this end, we derive a closed-form Stein correction coefficient for step-wise solver adjustment, enabling reference-free adaptation to local data geometry. We further establish a score-controlled perturbation bound under distributional shifts and provide a complementary Stein perspective on EDM-style parameterizations. Extensive experiments demonstrate that SteinDiff mitigates severe artifacts and improves generative quality across large-step inference settings.

Designing OLED molecules with targeted optical properties remains challenging due to the scarcity of high-quality data and the limited reliability of conditional control in generative models across chemical motifs. Here, we benchmark a token-conditioned autoregressive language model for OLED molecular generation in a realistic low-data regime. A GPT2 model is pretrained on large chemical corpora, augmented with discrete property tokens, and fine-tuned using multi-task optimisation. Conditioning targets vertical absorption energy and oscillator strength, with the HOMO-LUMO gap included as an auxiliary electronic descriptor. Generated molecules are evaluated at the TDDFT level to assess distributional fidelity and controllability. The generated library reproduces the dominant optical-property support of the training distribution while shifting towards lower molecular weight and fewer heavy atoms. Token-level control is consistently directional across conditioning bins, but is not fully orthogonal and exhibits local calibration irregularities. A chemotype-resolved analysis further shows that controllability depends strongly on local electronic environments: moderately conjugated aromatic-carbon motifs are associated with improved joint target satisfaction, whereas electron-withdrawing motifs, particularly aryl nitriles, show systematic red-shifting and reduced controllability. These results establish a quantitative benchmark for conditional OLED molecular generation and show that model reliability must be assessed in chemically meaningful subspaces rather than from aggregate property distributions alone.