We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.

Motivated by undetectable risks in generative AI, we study a general robust aggregation problem: how to aggregate several probability distributions to boost safety. We present consensus sampling, a black-box algorithm that, given k distributions, has risk competitive with the average risk of the safest $s$ while abstaining when there is insufficient agreement. This yields an architecture-agnostic approach to generative-model safety when the distributions are induced by models that can sample and evaluate output probabilities. We formalize the guarantee through R-robustness, which also bounds information leakage and adversarial influence. Inspired by robust statistics and the provable copyright protection algorithm of Vyas et al (2023), we show that while a standard mixture is vulnerable to one unsafe constituent, a pointwise-median construction provides robust intuition, and our efficient sampler is Pareto-optimal for the tradeoff between worst-case risk and abstention. Experiments on synthetic distributions and image generation illustrate the general mechanism and its motivating safety application. The method requires overlap among safe distributions, but it provides a model-agnostic way to inherit guarantees from an unknown reliable subset.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a standard recipe for post-training LLMs on reasoning tasks, with Group Relative Policy Optimization (GRPO) emerging as a leading approach. However, GRPO and its variants are inherently single-turn: they optimize from terminal rewards on isolated prompt-response pairs, leaving them poorly suited to agentic settings where models must iteratively refine solutions in response to environmental feedback. We introduce MURPHY, a multi-turn extension of GRPO for self-correcting code generation. MURPHY constructs feedback-conditioned rollout trees in which failed candidate solutions are paired with executor feedback and expanded into subsequent turns, and propagates rewards backward through the tree so that later successful refinements credit earlier attempts that surfaced informative feedback. We study two propagation strategies, Max Reward (MARS) and Mean Reward (MERS), and introduce post-rollout pruning mechanisms that reduce multi-turn optimization cost. Across three code generation benchmarks (HumanEval, MBPP, LiveCodeBench-v6) and two model families (Qwen3-1.7B/4B, OLMo-2-7B), MURPHY delivers up to 6% absolute pass@1 gains over the strongest prior multi-turn execution-feedback methods. Gains are largest on the Medium/Hard subset (+4.38/+4.20 at Iter-5), where iterative self-correction matters more.

High-stakes decisions informed by decision support systems require explicit evidence. While prior work focuses on short sufficient evidence, regulatory compliance and medical billing call for complete evidence: all relevant input tokens that support a decision. We formulate complete evidence extraction as a task and study it in a medical coding setting. Motivated by the Rashomon effect, we aggregate token-level evidence from multiple language models to increase evidence completeness. We perform a case study using existing equally-performing models, feature attributions, and a dataset with human-annotated evidence. Our results show that Rashomon ensembles significantly increase evidence recall while incurring only a small token overhead over individual models. Ensembles of only three models already outperform the best single model and recover information that individual models miss.

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: Adaptive Residual Kalman Smoother that operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

The rise of the machine learning (ML) model economy has intertwined markets for training datasets and pre-trained models. However, most pricing approaches still separate data and model transactions or rely on broker-centric pipelines that favor one side. Recent studies of data markets with externalities capture buyer interactions but do not yield a simultaneous and symmetric mechanism across data sellers, model producers, and model buyers. We propose a unified data-model coupled market that treats dataset and model trading as a single system. A supply-side mapping transforms dataset payments into buyer-visible model quotations, while a demand-side mapping propagates buyer prices back to datasets through Shapley-based allocation. Together, they form a closed loop that links four interactions: supply-demand propagation in both directions and mutual coupling among buyers and among sellers. We prove that the joint operator is a standard interference function (SIF), guaranteeing existence, uniqueness, and global convergence of equilibrium prices. Experiments demonstrate efficient convergence and improved fairness compared with broker-centric and one-sided baselines. The code is available on https://github.com/HongrunRen1109/Triple-Win-Pricing.

Persona conditioning is widely used to steer large language model (LLM) behavior, but it is unclear whether it induces stable behavioral structure or superficial variation. We propose a framework to measure consistent behavioral tendencies using situational judgment tests (SJTs), multidimensional item response theory (MIRT), and structured synthetic personas, treating responses as observations of latent behavioral variables. Across large-scale SJT and persona datasets, we find that persona-conditioned behaviors are stable across runs, latent trait scores predict external benchmarks (e.g., TruthfulQA, EmoBench), and MIRT reveals consistent latent structure. We validate these results through human annotation, benchmark evaluation, and internal consistency analyses. We interpret these traits not as human personality, but as stable behavioral tendencies expressed across contexts. Our results show that scenario-based psychometric evaluation provides a more reliable alternative to classical self-report approaches for assessing LLM behavior, and we release datasets to support further study.

Large language model (LLM) agents rely on external tools to solve complex tasks, but real-world toolsets often contain redundant tools with overlapping names and descriptions, introducing ambiguity and reducing selection accuracy. LLMs also face strict input context limits, preventing efficient consideration of large toolsets. To address these challenges, we propose ToolScope, which includes: (1) ToolScopeMerger with Auto-Correction to automatically audit and fix tool merges, reducing redundancy, and (2) ToolScopeRetriever to rank and select only the most relevant tools for each query, compressing toolsets to fit within context limits without sacrificing accuracy. Evaluations on three state-of-the-art LLMs and three open-source tool-use benchmarks show gains of 8.38% to 38.6% in tool selection accuracy, demonstrating ToolScope's effectiveness in enhancing LLM tool use.

Pairwise preference data have played an important role in the alignment of large language models (LLMs). Each sample of such data consists of a prompt, two different responses to the prompt, and a binary label indicating which of the two responses is better. The labels are usually annotated by professional human annotators. In this paper, we consider an alternative approach to collect pairwise preference data -- user annotation from comparison mode. With the increasingly wider adoption of LLMs among the population, users are contributing more and more of their preference labels through their daily interactions with the LLMs. The upside of such labels is that users are the best experts in judging the responses to their own queries/prompts, but the downside is the lack of quality control in these labels. In this paper, we consider a new idea of generating two responses from two different models or two different versions of the same model. The asymmetry allows us to make an inference of the user's data quality through our proposed user behavior model. We develop an expectation-maximization algorithm to estimate a latent quality factor of the user, and filter users' annotation data accordingly. The downstream task shows the effectiveness of our approach in both capturing the user behavior and data filtering for LLM alignment.

Safe reinforcement learning (RL) seeks to mitigate unsafe behaviors that arise from exploration during training by reducing constraint violations while maintaining task performance. Existing approaches typically rely on a single policy to jointly optimize reward and safety, which can cause instability due to conflicting objectives, or they use external safety filters that override actions and require prior system knowledge. In this paper, we propose a modular cost-aware regulator that scales the agent's actions based on predicted constraint violations, preserving exploration through smooth action modulation rather than overriding the policy. The regulator is trained to minimize constraint violations while avoiding degenerate suppression of actions. Our approach integrates seamlessly with off-policy RL methods such as SAC and TD3, and achieves state-of-the-art return-to-cost ratios on Safety Gym locomotion tasks with sparse costs, reducing constraint violations by up to 126 times while increasing returns by over an order of magnitude compared to prior methods.

Vision and language models frequently ignore semantically critical input edits, defaulting to pretraining priors. For example, models will confidently assert a five-legged dog has four legs; consequently, on the VLMBias benchmark, GPT 5.2 and Claude Sonnet 4.6 achieve only $4.6\%$ and $0\%$ accuracy, respectively. Existing methods address this problem through building up datasets that covers the underrepresented inputs to tune the policy function $π(y \mid x)$, where $x$ and $y$ refer to input prompts and responses, respectively. However, prompting baselines yield gains of under $3\%$ on VLMBias due to the low probability density of rare prompts. To bypass this bottleneck, we propose \emph{abductive preference learning} to optimize the abductive policy $π(x \mid y)$. We prove this amplifies forward policy improvements by a factor of $q(y)/p(x)$, where $p(\cdot)$ and $q(\cdot)$ denote the marginal probabilities of the prompt and response, yielding the largest gains on the rarest prompts. Furthermore, we demonstrate that for translation invariant pairwise preference learning methods, such as DPO, estimating $π(x \mid y)$ reduces to a structural data swap that compares prompts for a fixed response, requiring no architectural changes. Empirically, abductive preference learning delivers large gains on counterfactual sensitivity: on VLMBias, A-DPO raises accuracy from $3\%$ to $44\%$ ($14\times$), outperforming GPT-5.2 ($4.6\%$) and all closed-source VLMs except Gemini~3~Flash; on Inverse-IFEval, Multi-DPOP reaches $65$--$84\%$, surpassing GPT-5 ($73.7\%$) at the 9B scale while preserving IFBench, unlike DPO which degrades it by $8$--$12\%$.

Over the past couple of decades, many active learning acquisition functions have been proposed, leaving practitioners with an unclear choice of which to use. Bayesian-based active learning offers principled objectives with explainable intuition, including Expected Error Reduction (EER), Expected Predictive Information Gain (EPIG), and Bayesian Active Learning by Disagreements (BALD). A key challenge of such methods is the difficult scaling to large batch sizes, leading to either computational challenges (BatchBALD) or dramatic performance drops (top-$B$ selection). Here, using a particular formulation of Bayesian Decision Theory, we derive Partial Batch Label Sampling (ParBaLS) for the EPIG algorithm. We show experimentally for several datasets that ParBaLS EPIG gives superior performance for a fixed budget and Bayesian Logistic Regression on embeddings from large pre-trained models. Our code is available at https://github.com/ADDAPT-ML/ParBaLS.

Learning from demonstrations enables experts to teach robots complex tasks using interfaces such as kinesthetic teaching, joystick control, and sim-to-real transfer. However, these interfaces often constrain the expert's ability to demonstrate optimal behavior due to indirect control, setup restrictions, and hardware safety. For example, a joystick can move a robotic arm only in a 2D plane, even though the robot operates in a higher-dimensional space. As a result, the demonstrations collected by constrained experts lead to suboptimal performance of the learned policies. This raises a key question: Can a robot learn a better policy than the one demonstrated by a constrained expert? We address this by allowing the agent to go beyond direct imitation of expert actions and explore shorter and more efficient trajectories. We use the demonstrations to infer a state-only reward signal that measures task progress, and self-label reward for unknown states using temporal interpolation. Our approach outperforms common imitation learning in both sample efficiency and task completion time. On a real WidowX robotic arm, it completes the task in 12 seconds, 10x faster than behavioral cloning, as shown in real-robot videos on https://sites.google.com/view/constrainedexpert .

Test-Time Scaling (TTS) improves LLM reasoning by exploring multiple candidate responses and then operating over this set to find the best output. A tacit premise behind TTS is that sufficiently diverse candidate pools enhance reliability. In this work, we show that this assumption in TTS introduces a previously unrecognized failure mode. When candidate diversity is curtailed, even by a modest amount, TTS becomes much more likely to produce unsafe outputs. We present a reference-guided diversity reduction protocol (RefDiv) that serves as a diagnostic attack to stress test TTS pipelines. Through extensive experiments across open-source models (e.g. Qwen3, Mistral, Llama3.1, Gemma3) and two widely used TTS strategies (Monte Carlo Tree Search and Best-of-N), constraining diversity consistently signifies the rate at which TTS produces unsafe results. The effect is often stronger than that produced by prompts directly with high adversarial intent scores. This observed phenomenon also transfers across TTS strategies and to closed-source models (e.g. OpenAI o3-mini and Gemini-2.5-Pro), thus indicating that this is a general and extant property of TTS rather than a model-specific artifact. Additionally, we find that numerous widely used safety guardrail classifiers (e.g. Llama-Guard), are unable to flag the adversarial input prompts generated by RefDiv, demonstrating that existing defenses offer limited protection against this diversity-driven failure mode.

Despite advances in test-time scaling and diffusion finetuning, guidance for Auto-Regressive Diffusion Models (ARDMs) remains underexplored. We introduce an amortized framework that augments a pretrained ARDM with an offline-trained controller. By previewing future rollouts, the controller learns stepwise corrections that anticipate observations under a terminal-cost objective, yielding a reusable policy for guided generation. Motivated by a stochastic optimal control view of ARDM trajectories, our method injects small controls within each denoising sub-step while staying close to the pretrained dynamics. We study this approach for dataassimilation (DA) in chaotic spatiotemporal partial differential equations (PDEs), where existing methods are often computationally expensive and susceptible to forecast drift under sparse observations. At inference, DA becomes a feed-forward rollout with on-the-fly corrections, achieving an order-of-magnitude speedup over strong diffusion-based baselines. Across two canonical PDEs and a compact ECMWF Reanalysis v5 (ERA5) pilot spanning six observation regimes, our method consistently improves stability and accuracy over state-of-the-art alternatives, with similar improvements observed in a larger-scale GenCast study.

Test-Time Adaptation (TTA) methods are often computationally expensive, require a large amount of data for effective adaptation, or are brittle to hyperparameters. Based on a theoretical foundation of the geometry of the latent space, we are able to significantly improve the alignment between source and distribution-shifted samples by re-centering target data embeddings at the origin. This insight motivates NEO -- a hyperparameter-free fully TTA method, that adds no significant compute compared to vanilla inference. NEO is able to improve the classification accuracy of ViT-Base on ImageNet-C from 55.6% to 59.2% after adapting on just one batch of 64 samples. When adapting on 512 samples NEO beats all 7 TTA methods we compare against on ImageNet-C, ImageNet-R and ImageNet-S and beats 6/7 on CIFAR-10-C, while using the least amount of compute. NEO performs well on model calibration metrics and additionally is able to adapt from 1 class to improve accuracy on 999 other classes in ImageNet-C. On Raspberry Pi and Jetson Orin Nano devices, NEO reduces inference time by 63% and memory usage by 9% compared to baselines. Our results based on 3 ViT architectures and 4 datasets show that NEO can be used efficiently and effectively for TTA.

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in object trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant transformer for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory. Our codes, baseline models and datasets are available at https://github.com/Icarus1411/PAINET.

While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And crucially, what kinds of reasoning tasks do physicists want LLMs to assist with? To address these questions, we present the CritPt (Complex Research using Integrated Thinking - Physics Test, pronounced "critical point"), the first benchmark designed to test LLMs on unpublished, research-level reasoning tasks that broadly covers modern physics research areas, including condensed matter, quantum physics, atomic, molecular & optical physics, astrophysics, high energy physics, mathematical physics, statistical physics, nuclear physics, nonlinear dynamics, fluid dynamics and biophysics. CritPt consists of 71 composite research challenges designed to simulate full-scale research projects at the entry level, which are also decomposed to 190 simpler checkpoint tasks for more fine-grained insights. All problems are newly created by 50+ active physics researchers based on their own research. Every problem is hand-curated to admit a guess-resistant and machine-verifiable answer and is evaluated by an automated grading pipeline heavily customized for advanced physics-specific output formats. We find that while current state-of-the-art LLMs show early promise on isolated checkpoints, they remain far from being able to reliably solve full research-scale challenges: the best average accuracy among base models is only 5.7%, achieved by GPT-5 (high), moderately rising to around 10% when equipped with coding tools. Through the realistic yet standardized evaluation offered by CritPt, we highlight a large disconnect between current model capabilities and realistic physics research demands, offering a foundation to guide the development of scientifically grounded AI tools.

Time series forecasting occurs in a range of financial applications providing essential decision-making support to investors, regulatory institutions, and analysts. Unlike multivariate time series from other domains, stock time series exhibit industry correlation. Exploiting this kind of correlation can improve forecasting accuracy. However, existing methods based on hypergraphs can only capture industry correlation relatively superficially. These methods face two key limitations: they do not fully consider inter-industry lead-lag interactions, and they do not model multi-scale information within and among industries. This study proposes the Hermes framework for stock time series forecasting that aims to improve the exploitation of industry correlation by addressing these limitations. The framework integrates moving aggregation and multi-scale fusion modules in a hypergraph network. Specifically, to more flexibly capture the lead-lag relationships among industries, Hermes proposes a hyperedge-based moving aggregation module. This module incorporates a sliding window and utilizes dynamic temporal aggregation operations to consider lead-lag dependencies among industries. Additionally, to effectively model multi-scale information, Hermes employs cross-scale, edge-to-edge message passing to integrate information from different scales while maintaining the consistency of each scale. Experimental results on multiple real-world stock datasets show that Hermes outperforms existing state-of-the-art methods.

Large language models (LLMs) are commonly evaluated on challenging benchmarks such as AIME and Math500, where benchmark contamination can make memorized solutions appear as genuine reasoning. Existing detection methods largely rely on surface overlap, completion behavior, or final-output likelihood, and often degrade when inputs are simply rephrased. In this paper, we propose LogitTrace(Layerwise Logit Trajectories), a framework for analyzing memorization-like decision dynamics through intermediate logit trajectories. Instead of judging memorization only from the final answer, LogitTrace examines how model preferences emerge and stabilize across layers. We find that contaminated examples tend to show earlier commitment, while clean examples exhibit more gradual evidence accumulation. These trajectory signals allow a lightweight classifier to separate contaminated and clean examples across multiple models and input variants. Controlled LoRA injection experiments further show that repeated exposure to target samples induces similar trajectory patterns. Overall, our results suggest that LogitTrace provides evidence beyond surface overlap and final-output confidence, offering a useful lens for studying memorization-like behavior in LLMs.

Backpropagation through (neural) SDE solvers is traditionally approached in two ways: discretise-then-optimise, which offers accurate gradients but incurs prohibitive memory costs; and optimise-then-discretise, which achieves constant memory cost by solving an auxiliary backward SDE, but suffers from slower evaluation and gradient approximation errors. Algebraically reversible solvers promise both memory efficiency and gradient accuracy, yet existing methods such as Reversible Heun are often unstable under complex models and large step sizes, and their non-standard auxiliary-state structure obstructs extension to manifold-valued SDEs. Building on the recently introduced Explicit and Effectively Symmetric (EES) schemes - a class of stable, near-reversible explicit Runge--Kutta methods - we address both limitations of existing schemes. We extend EES schemes from ODEs to SDEs and show that they admit an efficient Williamson 2N-storage realisation. Bazavov's commutator-free construction then lifts these schemes to arbitrary Lie groups and homogeneous spaces. To our knowledge, this is the first explicit (near-)reversible integrator in this setting, unlocking the reversible adjoint approach for manifold-valued problems. On Euclidean neural SDE benchmarks, our schemes improve stability under stiff drift and large steps compared with other reversible solvers, while the commutator-free lift reduces memory by up to an order of magnitude on manifold-valued problems versus other baselines. These results establish effectively symmetric integration as a unified, geometry-aware foundation for memory-efficient and stable training of neural SDEs.

Off-policy reinforcement learning suffers from extrapolation errors when a learned policy selects actions that are weakly supported in the replay buffer. In this study, we address this issue by drawing an analogy to static friction. From this perspective, the replay buffer is represented as a smooth, low-dimensional action manifold, where the support directions correspond to the tangential component, while the normal component captures the dominant first-order extrapolation error. This decomposition reveals an intrinsic anisotropy in value sensitivity that naturally induces a stability condition analogous to a friction threshold. To mitigate deviations toward unsupported actions, we propose Frictional Q-Learning, an off-policy algorithm that encodes supported actions as tangent directions using a contrastive variational autoencoder. We further show that an orthonormal basis of the orthogonal complement corresponds to normal components under mild local isometry assumptions. Extensive empirical results on standard continuous-control benchmarks consistently demonstrate robust and stable performance compared with competitive baselines.

This paper studies fully decentralized cooperative multi-agent reinforcement learning, where each agent solely observes the states, its local actions, and the shared rewards. The inability to access other agents' actions often leads to non-stationarity during value function updates and relative overgeneralization during value function estimation, hindering effective cooperative policy learning. However, existing works fail to address both issues simultaneously, due to their inability to model the joint policy of other agents in a fully decentralized setting. To overcome this limitation, we propose a novel method named Dynamics-Aware Context (DAC), which formalizes the task, as locally perceived by each agent, as an Contextual Markov Decision Process, and further addresses both non-stationarity and relative overgeneralization through dynamics-aware context modeling. Specifically, DAC attributes the non-stationary local task dynamics of each agent to switches between unobserved contexts, each corresponding to a distinct joint policy. Then, DAC models the step-wise dynamics distribution using latent variables and refers to them as contexts. For each agent, DAC introduces a context-based value function to address the non-stationarity issue during value function update. For value function estimation, an optimistic marginal value is derived to promote the selection of cooperative actions, thereby addressing the relative overgeneralization issue. Experimentally, we evaluate DAC on various cooperative tasks (including matrix game, predator and prey, and SMAC), and its superior performance against multiple baselines validates its effectiveness.

Where do learning signals come from when there is no ground truth in post-training? We show that inference compute itself can serve as supervision. By generating parallel rollouts and converting them into reference estimates, models can learn without human labels-critically, even in non-verifiable domains like healthcare guidance where no programmatic checker exists. We call this framework Compute as Teacher (CaT) and it turns inference-time compute from parallel rollouts into supervision for RL training. The framework has two components: (1) reference estimation which aggregates rollouts into a pseudo-reference answer, and (2) reward derivation which converts that pseudo-reference into RL rewards. For (1), we explore a simple method we call synthesis, but the framework admits any aggregator. For (2), we introduce self-proposed rubrics for non-verifiable domains. These are binary, auditable criteria generated from the pseudo-reference and scored by an LLM judge. On HealthBench, models trained with CaT match or exceed inference-time aggregation quality while using 9x less test-time compute. Here, CaT also competes with learning from expert physician annotations, yielding up to +30% relative improvement over the initial policy. The framework extends naturally to verifiable rewards, matching the best existing baselines on MATH-500 in test-time RL and demonstrating 'drop-in' versatility across both types of domains.

Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) is a standard post-training recipe for improving Large Language Models (LLM) reasoning, but why it works remains unclear. We revisit the common claim that ``SFT memorizes, RL generalizes'' through checkpoint-wise analyses of in-distribution (ID) and out-of-distribution (OOD) reasoning. We find that OOD performance often peaks early during SFT and then declines despite continued improvement in ID reasoning. RL typically does not surpass this early SFT peak; rather, it restores OOD capability lost during later SFT, and only from a bounded range of SFT checkpoints. Further spectral analysis shows that this forgetting-and-recovery pattern correlates with rotations of singular vectors, while singular values remain largely stable. These findings suggest a more precise view of post-training dynamics: SFT can forget, RL can recover, and controlling singular-vector rotation may improve OOD robustness. Code is available at \href{https://github.com/jinhangzhan/RL\_Heals\_SFT.git}{https://github.com/jinhangzhan/RL\_Heals\_SFT}.

We present FractalPINN-Flow, an unsupervised deep learning framework for dense optical flow estimation that learns directly from consecutive grayscale frames without requiring ground truth. The architecture centers on the Fractal Deformation Network (FDN) - a recursive encoder-decoder inspired by fractal geometry and self-similarity. Unlike traditional CNNs with sequential downsampling, FDN uses repeated encoder-decoder nesting with skip connections to capture both fine-grained details and long-range motion patterns. The training objective is based on a classical variational formulation using total variation (TV) regularization. Specifically, we minimize an energy functional that combines $L^1$ and $L^2$ data fidelity terms to enforce brightness constancy, along with a TV term that promotes spatial smoothness and coherent flow fields. Experiments on synthetic and benchmark datasets show that FractalPINN-Flow produces accurate, smooth, and edge-preserving optical flow fields. The model is especially effective for high-resolution data and scenarios with limited annotations.

As large language models (LLMs) continue to grow in capability, so do the risks of harmful misuse through fine-tuning. While most prior studies assume that attackers rely on supervised fine-tuning (SFT) for such misuse, we systematically demonstrate that reinforcement learning (RL) enables adversaries to more effectively break safety alignment and facilitate more advanced harmful task assistance, under matched computational budgets. To counter this emerging threat, we propose TokenBuncher, the first effective defense specifically targeting RL-based harmful fine-tuning. TokenBuncher suppresses the foundation on which RL relies: model response entropy. By constraining entropy, RL-based fine-tuning can no longer exploit distinct reward signals to drive the model toward harmful behaviors. We realize this defense through entropy-as-reward RL and a Token Noiser mechanism designed to prevent the escalation of harmful capabilities. Extensive experiments across multiple models and RL algorithms show that TokenBuncher robustly mitigates harmful RL fine-tuning while preserving benign task performance and finetunability. Our results highlight that RL-based harmful fine-tuning poses a greater systemic risk than SFT, and that TokenBuncher provides an effective and general defense.

Multimodal representation learning has been largely driven by contrastive models such as CLIP, which learn a shared embedding space by aligning paired image-text samples. While effective for general-purpose representation learning, such models typically produce a single embedding per sample that is reused across different semantic relations and contexts. However, in many real-world applications, relevance between samples is inherently relation-dependent, with different semantic relations emphasizing different aspects of multimodal data. In this work, we propose Relation-Conditioned Multimodal Learning (RCML), a framework that treats semantic relations as explicit conditions of multimodal representation learning. Rather than producing relation-agnostic embeddings, RCML learns representations conditioned on natural-language relation descriptions, allowing the same sample to be represented differently under different relational contexts. The framework constructs relation-aware training pairs, introduces a relation-conditioned module to adapt embeddings to relation semantics, and employs a unified contrastive objective to jointly model cross-modal alignment and relation-induced inter-sample structure. Experiments on multiple datasets show that RCML consistently outperforms strong baselines on retrieval and classification tasks in zero-shot, fine-tuned, and out-of-domain settings, highlighting the effectiveness of leveraging semantic relations to guide multimodal representation learning.

The growing deployment of Large Language Models (LLMs) has raised concerns about their misuse in generating harmful or deceptive content. To address this issue, watermarking methods have been proposed to embed identifiable multi-bit messages into generated text for misuse tracing. However, existing methods often suffer from a fundamental trade-off between text quality and decoding accuracy. In particular, they have to restrict the size of the preferred token set (i.e., green list) during encoding to maintain a detectable watermark signal for decoding, which inevitably degrades generation quality. To improve this trade-off, we propose a novel message encoding paradigm called \textit{majority bit-aware encoding}, which relaxes the watermark signal strength from the green list size. This strategy allows for a strong watermark signal to be preserved in generated texts even when using a large green list. We introduce two instantiations of this paradigm: MajorMark and MajorMark$^{+}$, where the latter is specifically optimized for long messages. Extensive experiments on state-of-the-art LLMs demonstrate that our methods achieve higher decoding accuracy and superior text quality compared to prior baselines.

Chain-of-Thought (CoT) prompting has been shown to be effective in eliciting structured reasoning (i.e., CoT reasoning) from large language models (LLMs). Regardless of its popularity, recent studies expose its failures in some reasoning tasks, raising fundamental questions about the nature of CoT reasoning. In this work, we propose a data distribution lens to understand when and why CoT reasoning succeeds or fails. We hypothesize that CoT reasoning reflects a structured inductive bias learned from in-distribution data, enabling models to conditionally generate reasoning trajectories that approximate those observed during training. As such, the effectiveness of CoT reasoning is fundamentally governed by the nature and degree of distribution discrepancy between training data and test queries. Guided by this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To test the hypothesis, we introduce DataAlchemy, an abstract and fully controllable environment that trains LLMs from scratch and systematically probes them under various distribution conditions. Through rigorous controlled experiments, we reveal that CoT reasoning is a brittle mirage when it is pushed beyond training distributions, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.