The discovery of novel catalysts tailored for particular applications is a major challenge for the twenty-first century. Traditional methods for this include time-consuming and expensive experimental trial-and-error approaches in labs based on chemical theory or heavily computational first-principles approaches based on density functional theory. Recent studies show that deep learning models like graph neural networks (GNNs) can significantly speed up the screening of catalyst materials by many orders of magnitude, with very high accuracy and fidelity. In this work, we introduce Catalyst-Agent, a Model Context Protocol (MCP) server-based, LLM-powered AI agent. It can explore vast material databases using the OPTIMADE API, make structural modifications, calculate adsorption energies using Meta FAIRchem's UMA (GNN) model via FAIRchem's AdsorbML workflow and slab construction, and make useful material suggestions to the researcher in a closed-loop manner, including structural modifications to refine near-miss candidates. It is tested on three pivotal reactions: the oxygen reduction reaction (ORR), the nitrogen reduction reaction (NRR), and the CO2 reduction reaction (CO2RR). Catalyst-Agent achieves a success rate of 33-41% among all the materials it chooses and evaluates, and manages to converge in 1-4 trials per successful material on average. This work demonstrates the potential of AI agents to exercise their planning capabilities and tool use for autonomous catalyst screening workflows.

While Multi-Agent Systems (MAS) excel in complex reasoning, they suffer from the cascading impact of erroneous information from individual agents. Current solutions often resort to rigid structural engineering or expensive fine-tuning, limiting their adaptability. We propose AgentDropoutV2 (ADv2), a test-time rectify-or-reject pruning framework that dynamically optimizes MAS information flow. Acting as an active firewall, ADv2 intercepts agent outputs and employs a retrieval-augmented rectifier to iteratively correct errors. This rectification is guided by an indicator pool, which is constructed offline by distilling error patterns from historical MAS failure trajectories. Irreparable outputs are subsequently pruned to prevent error propagation. Empirical results demonstrate that ADv2 significantly boosts performance on both fixed and dynamic MAS frameworks, achieving average accuracy gains of 6.39 and 2.28 percentage points on extensive math and code benchmarks, respectively. Furthermore, ADv2 exhibits remarkable adaptivity, dynamically modulating rectification efforts based on task difficulty to resolve a wide spectrum of error patterns. Our code is released at https://github.com/TonySY2/AgentDropoutV2.

Generative Flow Networks (GFlowNets) learn to sample diverse candidates in proportion to a reward function, making them well-suited for scientific discovery, where exploring multiple promising solutions is crucial. Further extending GFlowNets to multi-objective settings has attracted growing interest as real-world applications often involve multiple, conflicting objectives. However, existing approaches require joint training for each combination of objectives, meaning that any change in the objective set necessitates retraining from scratch. We propose a framework that composes pre-trained GFlowNets at inference time, enabling rapid adaptation without fine-tuning or retraining. Importantly, our framework is flexible, capable of handling diverse reward combinations ranging from linear scalarization to complex nonlinear operators, which are often handled separately in previous literature. We prove that our method exactly recovers the target distribution for linear scalarization, and quantify the approximation quality for nonlinear operators through a distortion factor. Experiments on a synthetic 2D grid and real-world molecule generation tasks demonstrate that our approach achieves performance comparable to baselines.

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) reduce variance while maintaining tractability by leveraging low-dimensional individual state and action spaces and known transition dynamics to compute the exact expected return conditioned on Monte Carlo rollouts of common noise. However, HSMs have not been extended to partially observable settings. We propose Recurrent Structural Policy Gradient (RSPG), the first history-aware HSM for MFGs with public partial information. RSPG achieves an order-of-magnitude faster convergence than model-free RL methods while learning history-aware behaviour, unlike current HSMs. To facilitate research into MFGs, we also introduce MFAX, our JAX-based framework for MFGs that supports both analytic and sample-based mean-field updates. MFAX and usage examples can be found at https://clarisse-wibault.github.io/rspg/.

Current audio-visual large language models (AV-LLMs) are predominantly restricted to 2D perception, relying on RGB video and monaural audio. This design choice introduces a fundamental dimensionality mismatch that precludes reliable source localization and spatial reasoning in complex 3D environments. We address this limitation by presenting JAEGER, a framework that extends AV-LLMs to 3D space, to enable joint spatial grounding and reasoning through the integration of RGB-D observations and multi-channel first-order ambisonics. A core contribution of our work is the neural intensity vector (Neural IV), a learned spatial audio representation that encodes robust directional cues to enhance direction-of-arrival estimation, even in adverse acoustic scenarios with overlapping sources. To facilitate large-scale training and systematic evaluation, we propose SpatialSceneQA, a benchmark of 61k instruction-tuning samples curated from simulated physical environments. Extensive experiments demonstrate that our approach consistently surpasses 2D-centric baselines across diverse spatial perception and reasoning tasks, underscoring the necessity of explicit 3D modelling for advancing AI in physical environments. Our source code, pre-trained model checkpoints, and datasets are available at https://github.com/liuzhan22/JAEGER.

Structured dilated attention has an appealing inference-time efficiency knob: it reduces the FLOPs of attention and the KV cache size by a factor of the dilation size D, while preserving long-range connectivity. While prior work studies it by training each configuration from scratch, directly sparsifying a pretrained attention model into a dilated pattern leads to severe accuracy degradation, preventing flexible reuse across inference scenarios. We introduce RAT+, a dense-pretraining architecture that augments attention with full-sequence recurrence and active recurrence learning. A single RAT+ model is pretrained densely once and can then be flexibly switched at inference time to dilated attention (optionally with local windows) or hybrid layer/head compositions, requiring only a short 1B-token resolution adaptation rather than retraining separate sparse models. At 1.5B parameters trained on 100B tokens, RAT+ closely matches dense accuracy at D = 16, and drops by about 2-3 points at D = 64 on commonsense reasoning and LongBench tasks. We further scale to 2.6B and 7.6B parameters and observe even more promising performance (e.g., a 1-point average accuracy loss with a 64x reduction in attention FLOPs and KV cache size). Code is available at https://github.com/wimh966/rat-plus.

Large language models (LLMs) are increasingly applied as automatic evaluators for natural language generation assessment often using pairwise comparative judgements. Existing approaches typically rely on single judges or aggregate multiple judges assuming equal reliability. In practice, LLM judges vary substantially in performance across tasks and evaluation aspects, and their judgment probabilities may be biased and inconsistent. Furthermore, human-labelled supervision for judge calibration may be unavailable. We first empirically demonstrate that inconsistencies in LLM comparison probabilities exist and show that it limits the effectiveness of direct probability-based ranking. To address this, we study the LLM-asa-jury setting and propose BT-sigma, a judge-aware extension of the Bradley-Terry model that introduces a discriminator parameter for each judge to jointly infer item rankings and judge reliability from pairwise comparisons alone. Experiments on benchmark NLG evaluation datasets show that BT-sigma consistently outperforms averaging-based aggregation methods, and that the learned discriminators strongly correlate with independent measures of the cycle consistency of LLM judgments. Further analysis reveals that BT-sigma can be interpreted as an unsupervised calibration mechanism that improves aggregation by modelling judge reliability.

Generative model evaluation commonly relies on high-dimensional embedding spaces to compute distances between samples. We show that dataset representations in these spaces are affected by the hubness phenomenon, which distorts nearest-neighbor relationships and biases distance-based metrics. Building on the classical Iterative Contextual Dissimilarity Measure (ICDM), we introduce Generative ICDM (GICDM), a method to correct neighborhood estimation for both real and generated data. We introduce a multi-scale extension to improve empirical behavior. Extensive experiments on synthetic and real benchmarks demonstrate that GICDM resolves hubness-induced failures, restores reliable metric behavior, and improves alignment with human assessment.

Multi-Agent Systems (MAS) powered by Large Language Models have unlocked advanced collaborative reasoning, yet they remain bottlenecked by discrete text communication, which imposes runtime overhead and information quantization loss. While latent state transfer offers an alternative, existing approaches either assume homogeneous sender--receiver architectures or rely on pair-specific learned translators, limiting scalability across diverse model families with disjoint manifolds. We reconceptualize the visual interface of Vision-Language Models (VLMs), trained for natural images, as a continuous communication channel between heterogeneous agents, and instantiate this idea as the \textbf{Vision Wormhole}: a Universal Visual Codec maps reasoning traces into a shared continuous reference space and injects them into the receiver's visual pathway, yielding cross-architecture latent state transfer without per-pair translators. The framework adopts a hub-and-spoke topology that reduces alignment complexity from $O(N^2)$ to $O(N)$, and is trained by label-free teacher--student distillation against the text channel, requiring no parallel hidden-state supervision. Extensive experiments across heterogeneous VLM families (Qwen-VL, Gemma, SmolVLM2, LFM2.5-VL) and nine reasoning benchmarks show that the Vision Wormhole reduces end-to-end wall-clock time across most evaluated settings and yields positive macro-average $Δ$-accuracy.

Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for graph-structured data. A key design choice in GTs is the use of Graph Neural Network (GNN)-based positional encodings to incorporate structural information. In this work, we study GTs through the lens of manifold limit models for graph sequences and establish a theoretical connection between GTs with GNN positional encodings and Manifold Neural Networks (MNNs). Building on transferability results for GNNs under manifold convergence, we show that GTs inherit transferability guarantees from their positional encodings. In particular, GTs trained on small graphs provably generalize to larger graphs under mild assumptions. We complement our theory with extensive experiments on standard graph benchmarks, demonstrating that GTs exhibit scalable behavior on par with GNNs. To further show the efficiency in a real-world scenario, we implement GTs for shortest path distance estimation over terrains to better illustrate the efficiency of the transferable GTs. Our results provide new insights into the understanding of GTs and suggest practical directions for efficient training of GTs in large-scale settings.

Existing mainstream video customization methods focus on generating identity-consistent videos based on given reference images and textual prompts. Benefiting from the rapid advancement of joint audio-video generation, this paper proposes a more compelling new task: sync audio-video customization, which aims to synchronously customize both video identity and audio timbre. Specifically, given a reference image $I^{r}$ and a reference audio $A^{r}$, this novel task requires generating videos that maintain the identity of the reference image while imitating the timbre of the reference audio, with spoken content freely specifiable through user-provided textual prompts. To this end, we propose OmniCustom, a powerful DiT-based audio-video customization framework that can synthesize a video following reference image identity, audio timbre, and text prompts all at once in a zero-shot manner. Our framework is built on three key contributions. First, identity and audio timbre control are achieved through separate reference identity and audio LoRA modules that operate through self-attention layers within the base audio-video generation model. Second, we introduce a contrastive learning objective alongside the standard flow matching objective. It uses predicted flows conditioned on reference inputs as positive examples and those without reference conditions as negative examples, thereby enhancing the model ability to preserve identity and timbre. Third, we train OmniCustom on our constructed large-scale, high-quality audio-visual human dataset. Extensive experiments demonstrate that OmniCustom outperforms existing methods in generating audio-video content with consistent identity and timbre fidelity. Project page: https://omnicustom-project.github.io/page/.

Fine-tuning Large Language Models (LLMs) with Low-Rank Adaptation (LoRA) offers a resource-efficient way to personalize or specialize. However, LoRA is highly sensitive to hyperparameter choices, and exhaustive hyperparameter search is computationally expensive. To address this, we propose a Bayesian Optimization (BO) framework that leverages the domain knowledge of pre-trained LLMs to efficiently search for LoRA hyperparameters. Our approach repurposes a pre-trained LLM as a discrete-to-continuous mapping module to link hyperparameters and their domain knowledge to a continuous vector space, where BO is conducted. We design and control the mapping via language prompting, providing a domain-aware textual prompt that describes the relationships among hyperparameters and their respective roles. This allows us to explicitly inject domain knowledge about LoRA into the LLM in natural language. We also introduce an additional learnable token to capture residual information that is difficult to describe linguistically in the prompt. This aids BO to sample more high-performing hyperparameters. In addition, by leveraging the strong correlation observed between the performance obtained from full and subset training datasets in LoRA training regimes, we introduce proxy training and evaluation using a data subset. This significantly improves the efficiency of our method. We demonstrate that our hyperparameter, discovered with only about 30 iterations, achieves more than 20% performance improvement over standard hyperparameters found from about 45,000 combinations. Project page: https://baekseongeun.github.io/lora-bo/

Human conversation is organized by an implicit chain of thought and manifests as temporally structured conversational behaviors. Capturing this perceptual pathway is critical for building natural full-duplex interactive systems. We propose S-MARC (Streaming Causal Modeling and Reasoning for Conversation), a streaming, causal, and hierarchical framework for conversational behavior modeling and reasoning. By formalizing the intent-to-action pathway, S-MARC predicts high-level communicative functions and low-level interaction behaviors while modeling their causal and temporal dependencies. To support this setting, we construct a high-quality corpus that pairs controllable, event-rich duplex dialogue data with behavior labels. S-MARC organizes streaming predictions into a continuously evolving graph structure, generates concise justifications for its decisions, and dynamically optimizes its reasoning process. Experiments on synthetic and real duplex dialogues show that S-MARC achieves robust behavior detection, produces interpretable reasoning chains, and establishes a benchmark foundation for conversational reasoning in full-duplex spoken dialogue systems.

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack a reweighting procedure required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a framework for reduced-order generative modeling with importance sampling in coarse-grained coordinate space. CG-BGs generate samples using a flow-based model and reweight them using a learned potential of mean force (PMF). We show that the PMF can be learned from rapidly converged trajectories via enhanced sampling force matching. Experiments demonstrate that CG-BGs capture solvent-mediated interactions in highly reduced representations while substantially reducing computational cost relative to atomistic BGs, providing a practical route toward equilibrium sampling of larger molecular systems.

Looped Language Models (LoopLMs) perform multi-step latent reasoning prior to token generation and outperform conventional LLMs on reasoning benchmarks at smaller parameter budgets. However, attempts to further improve LoopLM reasoning with reinforcement learning have failed - standard objectives such as Group Relative Policy Optimization (GRPO) only assign credit to the final latent state, creating a fundamental mismatch with the model's internal computation. To resolve this, we introduce RLTT (Reward Latent Thought Trajectories), a reinforcement learning framework which distributes reward across the full latent reasoning trajectory. RLTT provides dense, trajectory-level credit assignment without relying on external verifiers and can directly replace GRPO with negligible overhead. Across extensive experiments with Ouro-1.4B/2.6B-Thinking under identical training and inference conditions, RLTT yields statistically significant improvements over GRPO on challenging mathematical reasoning benchmarks, improving mean accuracy over MATH-500, AIME24/26, and BeyondAIME by +5.8% on the 1.4B scale, and +10.9% on the 2.6B scale. Despite being trained exclusively on mathematics, RLTT also transfers effectively to non-mathematical reasoning benchmarks, demonstrating the effectiveness of trajectory-level credit assignment for reinforcement learning in LoopLMs. Code is available at https://github.com/jonwill8/RLTT.git.

Audio chaptering, the task of segmenting long-form audio into coherent sections, is increasingly important for navigating podcasts, lectures, and videos. Despite its relevance, research remains limited and text-based, leaving key questions unresolved about leveraging audio information, handling ASR errors, and transcript-free evaluation. We address these gaps through three contributions: (1) a systematic comparison between text-based models with acoustic features, a novel audio-only architecture (AudioSeg) operating on learned audio representations, and multimodal LLMs; (2) empirical analysis of factors affecting performance, including transcript quality, acoustic features, duration, and speaker composition; and (3) formalized evaluation protocols contrasting transcript-dependent text-space protocols with transcript-invariant time-space protocols. Our experiments on YTSeg reveal that AudioSeg substantially outperforms text-based approaches, pauses provide the largest acoustic gains, and MLLMs remain limited by context length and weak instruction following, yet MLLMs are promising on shorter audio.

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise do-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decodable early; (2) how influence propagates across steps and how this structure compares to explicit CoT; and (3) whether intermediate trajectories retain competing answer modes and how output-level commitment differs from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses, together with corresponding training/decoding objectives, as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

Being probabilistic models, during inference large language models (LLMs) display rare events: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage means that events completely unobserved during development are likely to become prominent in deployment. Here we present an end-to-end framework for the systematic analysis of rare events in LLMs. We provide a practical implementation spanning theory, efficient generation strategies, probability estimation and error analysis, which we illustrate with concrete examples. We outline extensions and applications to other models and contexts, highlighting the generality of the concepts and techniques presented here.

Autoregressive large language models (LLMs) deliver strong performance but require inherently sequential decoding, leading to high inference latency and poor GPU utilization. Speculative decoding mitigates this bottleneck by using a fast draft model whose outputs are verified in parallel by the target LLM; however, existing methods still rely on autoregressive drafting, which remains sequential and limits practical speedups. Diffusion LLMs offer a promising alternative by enabling parallel generation, but current diffusion models typically underperform compared with autoregressive models. In this paper, we introduce DFlash, a speculative decoding framework that employs a lightweight block diffusion model for parallel drafting. By generating draft tokens in a single forward pass and conditioning the draft model on context features extracted from the target model, DFlash enables efficient drafting with high-quality outputs and higher acceptance rates. Experiments show that DFlash achieves over 6x lossless acceleration across a range of models and tasks, delivering up to 2.5x higher speedup than the state-of-the-art speculative decoding method EAGLE-3.

Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schrödinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.

This paper proposes FedNMap, a normal map-based method for composite federated learning, where the objective consists of a smooth loss and a possibly nonsmooth regularizer. FedNMap leverages a normal map-based update scheme to handle the nonsmooth term and incorporates a local correction strategy to mitigate the impact of data heterogeneity across clients. Under standard assumptions, including smooth local losses, weak convexity of the regularizer, and bounded stochastic gradient variance, FedNMap achieves linear speedup with respect to both the number of clients and the number of local updates for nonconvex losses, both with and without the Polyak-Łojasiewicz condition. To the best of our knowledge, this is the first algorithm establishing linear speedup for nonconvex composite federated learning. Numerical experiments corroborate our theoretical findings and demonstrate the linear speedup of FedNMap.

The design of Analog and Mixed-Signal (AMS) integrated circuits remains heavily reliant on expert knowledge, with transistor sizing a major bottleneck due to nonlinear behavior, high-dimensional design spaces, and strict performance constraints. Existing Electronic Design Automation (EDA) methods typically frame sizing as static black-box optimization, resulting in inefficient and less robust solutions. Although Large Language Models (LLMs) exhibit strong reasoning abilities, they are not suited for precise numerical optimization in AMS sizing. To address this gap, we propose AutoSizer, a reflective LLM-driven meta-optimization framework that unifies circuit understanding, adaptive search-space construction, and optimization orchestration in a closed loop. It employs a two-loop optimization framework, with an inner loop for circuit sizing and an outer loop that analyzes optimization dynamics and constraints to iteratively refine the search space from simulation feedback. We further introduce AMS-SizingBench, an open benchmark comprising 24 diverse AMS circuits in SKY130 CMOS technology, designed to evaluate adaptive optimization policies under realistic simulator-based constraints. AutoSizer experimentally achieves higher solution quality, faster convergence, and higher success rate across varying circuit difficulties, outperforming both traditional optimization methods and existing LLM-based agents.

Chain-of-thought (CoT) reasoning has become a central mechanism for eliciting multi-step reasoning in Large Language Models (LLMs). Yet recent evidence presents a tension: hidden states appear to already encode future reasoning before CoT fully unfolds, while explicit steps still remain crucial for tasks requiring compositional computation. To deepen the understanding between LLM's internal states and its verbalized reasoning trajectories, we investigate the latent planning strength of LLMs, through our probing method, Tele-Lens, applying to hidden states across diverse task domains. Our empirical results indicate that LLMs exhibit a myopic horizon, primarily conducting incremental transitions without precise global planning. Leveraging this characteristic, we propose a hypothesis on enhancing uncertainty estimation of CoT, which we validate that a sparse set of pivot positions can effectively represent the uncertainty of the entire path. We further underscore the significance of exploiting CoT dynamics, and demonstrate that automatic recognition of CoT bypass can be achieved without performance degradation. Our code, data and models are released at https://github.com/lxucs/tele-lens.

LLM-driven agents excel at sequential decision-making but often rely on on-the-fly reasoning, re-deriving solutions even in recurring scenarios. This insufficient experience reuse leads to computational redundancy and instability. To bridge this gap, we propose Skill-Pro, a framework enabling agents to autonomously learn reusable procedural skills from interaction experiences without parameter updates. By formalizing a Skill-MDP, Skill-Pro transforms passive episodic narratives into executable Skills defined by activation, execution, and termination conditions to ensure executability. To achieve reliable reusability without capability degradation, we introduce Non-Parametric PPO, which leverages semantic gradients for high-quality candidate generation and a PPO Gate for robust Skill verification. Through score-based maintenance, Skill-Pro sustains compact, high-quality procedural memory. Experimental results across in-domain, cross-task, and cross-agent scenarios demonstrate that Skill-Pro achieves superior reuse rates and significant gains with extreme memory compression. Visualized evolutionary trajectories and Skill distributions further reveal how Skill-Pro transparently accumulates, refines, and reuses procedural knowledge to facilitate long-term autonomy.

Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian distributions, but inherently favor dense representations and fail to capture the key property of sparsity observed in efficient representations. We introduce Rectified Distribution Matching Regularization (RDMReg), a sliced two-sample distribution-matching loss that aligns representations to a Rectified Generalized Gaussian (RGG) distribution. RGG enables explicit control over expected $\ell_0$ norm through rectification, while its continuous truncated component admits a maximum-entropy characterization under expected $\ell_p$ norm and support constraints. Equipping JEPAs with RDMReg yields Rectified LpJEPA, which strictly generalizes prior Gaussian-based JEPAs. Empirically, Rectified LpJEPA learns sparse, non-negative representations with favorable sparsity--performance trade-offs and competitive downstream performance on image classification benchmarks, showing that RDMReg can enforce sparsity while preserving task-relevant information.

We consider the problem of unsupervised skill segmentation and hierarchical structure discovery in reinforcement learning. While recent approaches have sought to segment trajectories into reusable skills or options, most rely on action labels, rewards, or handcrafted annotations, limiting their applicability. We propose a method that segments unlabelled trajectories into skills and induces a hierarchical structure over them using a grammar-based approach. The resulting hierarchy captures both low-level behaviours and their composition into higher-level skills. We evaluate our approach in high-dimensional, pixel-based environments, including Craftax and the full, unmodified version of Minecraft. Using metrics for skill segmentation, reuse, and hierarchy quality, we find that our method consistently produces more structured and semantically meaningful hierarchies than existing baselines. Furthermore, as a proof of concept, we demonstrate that these discovered hierarchies accelerate and stabilise learning on downstream reinforcement learning tasks.

Real-world federated systems seldom operate on static data: input distributions drift while privacy rules forbid raw-data sharing. We study this setting as Federated Domain-Incremental Learning (FDIL), where (i) clients are heterogeneous, (ii) tasks arrive sequentially with shifting domains, yet (iii) the label space remains fixed. Two theoretical pillars remain missing for FDIL under realistic deployment: a guarantee of backward knowledge transfer (BKT) and a convergence rate that holds across the sequence of all tasks with partial participation. We introduce SPECIAL (Server-Proximal Efficient Continual Aggregation for Learning), a simple, memory-free FDIL algorithm that adds a single server-side ``anchor'' to vanilla FedAvg: in each round, the server nudges the uniformly sampled participated clients update toward the previous global model with a lightweight proximal term. This anchor curbs cumulative drift without replay buffers, synthetic data, or task-specific heads, keeping communication and model size unchanged. Our theory shows that SPECIAL (i) preserves earlier tasks: a BKT bound caps any increase in prior-task loss by a drift-controlled term that shrinks with more rounds, local epochs, and participating clients; and (ii) learns efficiently across all tasks: the first communication-efficient non-convex convergence rate for FDIL with partial participation, O((E/NT)^(1/2)), with E local epochs, T communication rounds, and N participated clients per round, matching single-task FedAvg while explicitly separating optimization variance from inter-task drift. Experimental results further demonstrate the effectiveness of SPECIAL.

Current LLM post-training methods optimize complete reasoning trajectories through Supervised Fine-Tuning (SFT) followed by outcome-based Reinforcement Learning (RL). While effective, a closer examination reveals a fundamental gap: this approach does not align with how humans actually solve problems. Human cognition naturally decomposes problem-solving into two distinct stages: first acquiring abstract strategies (i.e., meta-knowledge) that generalize across problems, then adapting them to specific instances. In contrast, by treating complete trajectories as basic units, current methods are inherently problem-centric, entangling abstract strategies with problem-specific execution. To address this misalignment, we propose a cognitively-inspired framework that explicitly mirrors the two-stage human cognitive process. Specifically, Chain-of-Meta-Thought CoMT focuses supervised learning on abstract reasoning patterns without specific executions, enabling acquisition of generalizable strategies. Confidence-Calibrated Reinforcement Learning (CCRL) then optimizes task adaptation via confidence-aware rewards on intermediate steps, preventing overconfident errors from cascading and improving execution reliability. Experiments across four models and ten benchmarks show 2.10% and 3.86% improvements in-distribution and out-of-distribution respectively over standard methods, while remaining highly robust to variations in teacher model selection, optimization methods, and symbolic perturbations.

We present a unified framework for quantifying the similarity between representations through the lens of \textit{usable} information, offering a rigorous theoretical and empirical synthesis across three key dimensions. First, addressing functional similarity, we establish a formal link between stitching performance and conditional mutual information. We further reveal that stitching is inherently asymmetric, demonstrating that robust functional comparison necessitates a bidirectional analysis rather than a unidirectional mapping. Second, concerning representational similarity, we find that reconstruction-based metrics and standard tools (e.g., CKA, RSA) act as estimators of usable information under specific constraints. Crucially, we show that similarity is relative to the capacity of the predictive family: representations that appear distinct to a rigid observer may be identical to a more expressive one. Third, we demonstrate that representational similarity is sufficient but not necessary for functional similarity. We unify these concepts through a task-granularity hierarchy: similarity on a complex task guarantees similarity on any coarser derivative, establishing representational similarity as the limit of maximum granularity: input reconstruction.

Machine unlearning seeks to remove the influence of specific training data from a model, a need driven by privacy regulations and robustness concerns. Existing approaches typically modify model parameters, but such updates can be unstable, computationally costly, and limited by local approximations. We introduce Representation Unlearning, a framework that performs unlearning directly in the model's representation space. Instead of modifying model parameters, we learn a transformation over representations that imposes an information bottleneck: maximizing mutual information with retained data while suppressing information about data to be forgotten. We derive variational surrogates that make this objective tractable and show how they can be instantiated in two practical regimes: when both retain and forget data are available, and in a zero-shot setting where only forget data can be accessed. Experiments across several benchmarks demonstrate that Representation Unlearning achieves more reliable forgetting, better utility retention, and greater computational efficiency than parameter-centric baselines.