ICLR 2026 Papers

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

Stochastic gradient descent with momentum (SGDM) is widely used in machine learning, yet high-probability learning bounds for SGDM in non-convex settings remain scarce. In this paper, we provide high-probability convergence bounds and generalization bounds for SGDM. First, we establish such bounds for the gradient norm in the general non-convex case. The resulting convergence bounds are tighter than existing theoretical results, and to the best of our knowledge, the obtained generalization bounds are the first ones for SGDM. Next, under the Polyak-{\L}ojasiewicz condition, we derive bounds for the function-value error instead of the gradient norm, and the corresponding learning rates are faster than in the general non-convex case. Finally, by additionally assuming a mild Bernstein condition on the gradient, we obtain even sharper generalization bounds whose learning rates can reach $\widetilde{\mathcal{O}}(1/n^2)$ in the low-noise regime, where $n$ is the sample size. Overall, we provide a systematic study of high-probability learning bounds for non-convex SGDM.

Multimodal large language models (MLLMs) have achieved remarkable progress in vision–language reasoning, yet they remain vulnerable to hallucination, where generated content deviates from the visual evidence. Existing mitigation strategies either demand costly supervision during training or introduce additional latency at inference. Recent vision-enhancement methods attempt to address this by reinforcing visual tokens during decoding, but they typically inject all tokens indiscriminately, leading to interference from background regions and distracting the model from critical cues. To overcome this challenge, we propose an **A**daptive v**I**sual **R**einforcement framework for MLLMs, dubbed as **AIR**. AIR consists of two main components: prototype-based token reduction, which condenses the large pool of visual tokens into a compact subset to suppress redundancy, and OT-guided patch reinforcement, which quantifies the alignment between hidden state and patch embeddings to selectively integrate the most consistent patches into the feed-forward layers. As a result, AIR enhances the model’s reliance on salient visual information and effectively mitigates hallucination. Extensive experiments across representative MLLMs demonstrate that AIR substantially reduces hallucination while preserving general capabilities, establishing it as an effective and independent solution for building reliable MLLMs.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 22.6 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5\% of cases.

Deep neural networks often exhibit substantial disparities in class-wise accuracy, even when trained on class-balanced data—posing concerns for reliable deployment. While prior efforts have explored empirical remedies, a theoretical understanding of such performance disparities in classification remains limited. In this work, we present Margin Regularization for performance disparity Reduction ( $MR^2$ ), a theoretically principled regularization for classification by dynamically adjusting margins in both the logit and representation spaces. Our analysis establishes a novel margin-based, class-sensitive generalization bound that reveals how per-class feature variability contributes to error, motivating the use of larger margins for ''hard'' classes. Guided by this insight,$MR^2$ optimizes per-class logit margins proportional to feature spread and penalizes excessive representation margins to enhance intra-class compactness. Experiments on seven datasets—including ImageNet—and diverse pre-trained backbones (MAE, MoCov2, CLIP) demonstrate demonstrate that our $MR^2$ not only improves overall accuracy but also significantly boosts ''hard'' class performance without trading off ''easy'' classes, thus reducing the performance disparities. Codes are available in https://github.com/BeierZhu/MR2.

Large Language Models (LLMs) have recently emerged as promising agents for Traffic Signal Control (TSC) due to their strengths in reasoning and generalization. However, current LLM-based approaches treat intersections as independent agents without inter-intersection cooperation, limiting their effectiveness in network-wide optimization. To address this gap, we propose CoLLMLight, the first cooperative LLM agent framework for network-wide traffic signal control. CoLLMLight enables agents to perform in-depth spatiotemporal reasoning for cooperation, while ensuring real-time responsiveness through an asynchronous cooperative decision architecture. The reasoning process runs asynchronously, deriving cooperative control guidance from dynamic interactions among intersections. This guidance is cached and incorporated as contextual input for real-time signal decisions. To enhance cooperation quality while ensuring reasoning efficiency, we propose cost-aware cooperation optimization. It first applies adaptive reasoning chain optimization to enable the LLM to adjust its reasoning depth according to traffic complexity. The model is then refined with reinforcement learning using reward signals that promote network-wide performance while penalizing excessive reasoning. Extensive experiments on four real-world traffic networks demonstrate that CoLLMLight consistently outperforms existing methods, achieving more effective and generalizable cooperation while maintaining real-time responsiveness and efficient token usage.

Large language models (LLMs) are moving beyond static uses and are now powering agents that learn during their interaction with external environments. For example, agents can learn reusable skills while navigating web pages or toggling new tools. However, existing methods for skill learning often create skills that are over-specialized to a single website and fail to generalize. We introduce PolySkill, a new framework that enables agents to learn generalizable and compositional skills. The core idea, inspired by polymorphism in software engineering, is to decouple a skill's abstract goal (*what* it accomplishes) and its concrete implementation (*how* it is executed). Experiments show that our method (1) improves skill reuse by 1.7x on seen websites and (2) boosts success rates by up to 9.4\% on Mind2Web and 13.9\% on unseen websites, while reducing steps by over 20\%. (3) In self-exploration settings without specified tasks, our framework improves the quality of proposed tasks and enables agents to learn generalizable skills that work across different sites. By enabling the agent to identify and refine its own goals, the \ours enhance the agent a better curriculum, leading to the acquisition of more generalizable skills compared to baseline methods. This work provides a practical path toward building agents capable of continual learning in adaptive environments.

Concept Bottleneck Generative Models (CBGMs) incorporate a human-interpretable concept bottleneck layer, which makes them interpretable and steerable. However, designing such a layer for generative models poses the same challenges as for concept bottleneck models in a supervised context, if not greater ones. Deterministic mappings from the model inner representations to soft concepts in existing CBGMs: (i) limit steerable generation to modifying concepts in existing inputs; and, more importantly, (ii) are susceptible to *concept leakage*, which hinders their steerability. To address these limitations, we first introduce the Variational Hard Concept Bottleneck (VHCB) layer. The VHCB maps probabilistic estimates of binary latent variables to hard concepts, which have been shown to mitigate leakage. Remarkably, its probabilistic formulation enables direct generation from a specified set of concepts. Second, we propose a systematic evaluation framework for assessing the steerability of CBGMs across various tasks (e.g., activating and deactivating concepts). Our framework which allows us to empirically demonstrate that the VHCB layer consistently improves steerability.

Inherently, robotic manipulation tasks are history-dependent: leveraging past context could be beneficial. However, most existing Vision-Language-Action models (VLAs) have been designed without considering this aspect, i.e., they rely solely on the current observation, ignoring preceding context. In this paper, we propose HAMLET, a scalable framework to adapt VLAs to attend to the historical context during action prediction. Specifically, we introduce moment tokens that compactly encode perceptual information at each timestep. Their representations are initialized with time-contrastive learning, allowing them to better capture temporally distinctive aspects. Next, we employ a lightweight memory module that integrates the moment tokens across past timesteps into memory features, which are then leveraged for action prediction. Through empirical evaluation, we show that HAMLET successfully transforms a state-of-the-art VLA into a history-aware policy, especially demonstrating significant improvements on long-horizon tasks that require historical context. In particular, on top of GR00T N1.5, HAMLET achieves an average success rate of 76.4% on history-dependent real-world tasks, surpassing the baseline performance by 47.2%. Furthermore, HAMLET pushes prior art performance from 64.1% to 66.4% on RoboCasa Kitchen (100-demo setup) and from 95.6% to 97.7% on LIBERO, highlighting its effectiveness even under generic robot-manipulation benchmarks.

We present GRL-SNAM, a geometric reinforcement learning framework for Simultaneous Navigation and Mapping in unknown environments. GRL-SNAM differs from traditional SLAM and other reinforcement learning methods by relying exclusively on local sensory observations without constructing a global map. Our approach formulates navigation and mapping as coupled dynamics on generalized Hamiltonian manifolds: sensory inputs are translated into local energy landscapes that encode reachability, obstacle barriers, and deformation constraints, while policies for sensing, planning, and reconfiguration evolve stagewise under Differential Policy Optimization (DPO). A reduced Hamiltonian serves as an adaptive score function, updating kinetic/potential terms, embedding barrier constraints, and continuously refining trajectories as new local information arrives. We evaluate GRL-SNAM on 2D deformable navigation tasks, where a hyperelastic robot learns to squeeze through narrow gaps, detour around obstacles, and generalize to unseen environments. We evaluate GRL-SNAM on procedurally generated 2D deformable–robot tasks comparing against local reactive baselines (PF, CBF, staged DWA) and global A* references (rigid, clearance-aware) under identical stagewise sensing constraints. GRL-SNAM shows superior path quality while using the minimal map coverage, preserves clearance, generalizes to unseen layouts, and demonstrates that Hamiltonian-structured RL enables high-quality navigation through minimal exploration via local energy refinement rather than global mapping.

Large Vision-Language Models (LVLMs) have demonstrated capabilities in multimodal understanding, yet their vulnerability to adversarial attacks raises significant concerns. To achieve practical attacking, this paper aims at efficient and transferable untargeted attacks under limited perturbation sizes. Considering this objective, white‑box attacks require full‑model gradients and task‑specific labels, making costs scale with tasks, while black‑box attacks rely on proxy models, typically requiring large perturbation sizes and elaborate transfer strategies. Given the centrality and widespread reuse of the vision encoder in LVLMs, we adopt a gray‑box setting that targets the vision encoder alone for efficient but effective attacking. We theoretically establish the feasibility of vision‑encoder‑only attacks, laying the foundation for our gray‑box setting. Based on this analysis, we propose perturbing patch tokens rather than the class token, informed by both theoretical and empirical insights. We generate adversarial examples by minimizing the cosine similarity between clean and perturbed visual features, without accessing the subsequent models, tasks, or labels. This significantly reduces computational overhead while eliminating the task and label dependence. VEAttack has achieved a performance degradation of 94.5% on image caption task and 75.7% on visual question answering task. We also reveal some key observations to provide insights into LVLM attack/defense: 1) hidden layer variations of LLM, 2) token attention differential, 3) Möbius band in transfer attack, 4) low sensitivity to attack steps.

Precise recognition, editing, and generation of molecules are essential prerequisites for both chemists and AI systems tackling various chemical tasks. We present MolLangBench, a comprehensive benchmark designed to evaluate fundamental molecule-language interface tasks: language-prompted molecular structure recognition, editing, and generation. To ensure high-quality, unambiguous, and deterministic outputs, we construct the recognition tasks using automated cheminformatics tools, and curate editing and generation tasks through rigorous expert annotation and validation. MolLangBench supports the evaluation of models that interface language with different molecular representations, including linear strings, molecular images, and molecular graphs. Evaluations of state-of-the-art models reveal significant limitations: the strongest model (GPT-5) achieves $86.2$\% and $85.5$\% accuracy on recognition and editing tasks, which are intuitively simple for humans, and performs even worse on the generation task, reaching only $43.0$\% accuracy. These results highlight the shortcomings of current AI systems in handling even preliminary molecular recognition and manipulation tasks. We hope MolLangBench will catalyze further research toward more effective and reliable AI systems for chemical applications. The dataset and code can be accessed at https://huggingface.co/datasets/ChemFM/MolLangBench and https://github.com/TheLuoFengLab/MolLangBench, respectively.

Fingerprinting Large Language Models (LLMs) is essential for provenance verification and model attribution. Existing methods typically extract post-hoc signatures based on training dynamics, data exposure, or hyperparameters—properties that only emerge after training begins. In contrast, we propose a stronger and more intrinsic notion of LLM fingerprinting: **SeedPrints**, a method that leverages random initialization biases as persistent, seed-dependent identifiers present even before training. We show that untrained models exhibit reproducible token selection biases conditioned solely on their parameters at initialization. These biases are stable and measurable throughout training, enabling our statistical detection method to recover a model’s lineage with high confidence. Unlike prior techniques, unreliable before convergence and vulnerable to distribution shifts, **SeedPrints** remains effective across all training stages and robust under domain shifts or parameter modifications. Experiments on LLaMA-style and Qwen-style models show that SeedPrints achieves seed-level distinguishability and can provide birth-to-lifecycle identity verification akin to a biometric fingerprint. Evaluations on large-scale pretrained models and fingerprinting benchmarks further confirm its effectiveness under practical deployment scenarios. These results suggest that initialization itself imprints a unique and persistent identity on neural language models, forming a true ``Galtonian'' fingerprint.

In-context learning (ICL) is a central capability of Transformer models, but the structures in data that enable its emergence and govern its robustness remain poorly understood. In this work, we study how the structure of pretraining tasks governs generalization in ICL. Using a solvable model for ICL of linear regression by linear attention, we derive an exact expression for ICL generalization error in high dimensions under arbitrary pretraining–testing task covariance mismatch. This leads to a new alignment measure that quantifies how much information about the pretraining task distribution is useful for inference at test time. We show that this measure directly predicts ICL performance not only in the solvable model but also in nonlinear Transformers. Our analysis further reveals a tradeoff between specialization and generalization in ICL: depending on task distribution alignment, increasing pretraining task diversity can either improve or harm test performance. Together, these results identify train-test task alignment as a key determinant of generalization in ICL.

What happens when multiple compression methods are combined—does the order in which they are applied matter? Joint model compression has emerged as a powerful strategy to achieve higher efficiency by combining multiple methods such as pruning and quantization. A central but underexplored factor in joint model compression is the compression order, or the sequence of different methods within the compression pipeline. Most prior studies have either sidestepped the issue by assuming orthogonality between techniques, while a few have examined them only in highly constrained cases. Consequently, the broader role of compression order in shaping model performance remains poorly understood. In this paper, we address the overlooked problem of compression order and provide both theoretical and empirical analysis. We formulate the problem of optimizing the compression order and introduce the Progressive Intensity Hypothesis, which states that weaker perturbations should precede stronger ones. We provide theoretical guarantees showing that the relative benefit of one order increases with the underlying performance gap. Extensive experiments on both language and vision models validate the hypothesis, and further show its generality to broader setups such as multi-stage compression and mixed-precision quantization.

Recent advances in driving-scene generation and reconstruction have demonstrated significant potential for enhancing autonomous driving systems by producing scalable and controllable training data. Existing generation methods primarily focus on synthesizing diverse and high-fidelity driving videos; however, due to limited 3D consistency and sparse viewpoint coverage, they struggle to support convenient and high-quality novel-view synthesis (NVS). Conversely, recent 3D/4D reconstruction approaches have significantly improved NVS for real-world driving scenes, yet inherently lack generative capabilities. To overcome this dilemma between scene generation and reconstruction, we propose \textbf{WorldSplat}, a novel feed-forward framework for 4D driving-scene generation. Our approach effectively generates consistent multi-track videos through two key steps: ((i)) We introduce a 4D-aware latent diffusion model integrating multi-modal information to produce pixel-aligned 4D Gaussians in a feed-forward manner. ((ii)) Subsequently, we refine the novel view videos rendered from these Gaussians using a enhanced video diffusion model. Extensive experiments conducted on benchmark datasets demonstrate that \textbf{WorldSplat} effectively generates high-fidelity, temporally and spatially consistent multi-track novel view driving videos.

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. However, the convergence rate of GD for training two-layer neural networks exhibits poor dependence on the sample size and the Gram matrix, leading to a slow training process. In this paper, we show that for training two-layer $\text{ReLU}^3$ Physics-Informed Neural Networks (PINNs), the learning rate can be improved from the smallest eigenvalue of the limiting Gram matrix to the reciprocal of the largest eigenvalue, implying that GD actually enjoys a faster convergence rate. Despite such improvements, the convergence rate is still tied to the least eigenvalue of the Gram matrix, leading to slow convergence. We then develop the positive definiteness of Gram matrices with general smooth activation functions and provide the convergence analysis of natural gradient descent (NGD) in training two-layer PINNs, demonstrating that the maximal learning rate can be $\mathcal{O}(1)$ and at this rate, the convergence rate is independent of the Gram matrix. In particular, for smooth activation functions, the convergence rate of NGD is quadratic. Numerical experiments are conducted to verify our theoretical results.

Large vision-language models have achieved remarkable progress in visual reasoning, yet most existing systems rely on single-step or text-only reasoning, limiting their ability to iteratively refine understanding across multiple visual contexts. To address this limitation, we introduce a new multi-round visual reasoning benchmark with training and test sets spanning both detection and segmentation tasks, enabling systematic evaluation under iterative reasoning scenarios. We further propose RegionReasoner, a reinforcement learning framework that enforces grounded reasoning by requiring each reasoning trace to explicitly cite the corresponding reference bounding boxes, while maintaining semantic coherence via a global–local consistency reward. This reward extracts key objects and nouns from both global scene captions and region-level captions, aligning them with the reasoning trace to ensure consistency across reasoning steps. RegionReasoner is optimized with structured rewards combining grounding fidelity and global–local semantic alignment. Experiments on detection and segmentation tasks show that RegionReasoner-7B, together with our newly introduced benchmark RegionDial-Bench, considerably improves multi-round reasoning accuracy, spatial grounding precision, and global–local consistency, establishing a strong baseline for this emerging research direction.

Kirkpatrick et al. [ALT 2019] and Fallat et al. [JMLR 2023] introduced non-clashing teaching and proved that it is the most efficient batch machine teaching model satisfying the collusion-avoidance benchmark established in the seminal work of Goldman and Mathias [COLT 1993]. Recently, (positive) non-clashing teaching was thoroughly studied for balls in graphs, yielding numerous algorithmic and combinatorial results. In particular, Chalopin et al. [COLT 2024] and Ganian et al. [ICLR 2025] gave an almost complete picture of the complexity landscape of the positive variant, showing that it is tractable only for restricted graph classes due to the non-trivial nature of the problem and concept class. In this work, we consider (positive) non-clashing teaching for closed neighborhoods in graphs. This concept class is not only extensively studied in various related contexts, but it also exhibits broad generality, as any finite binary concept class can be equivalently represented by a set of closed neighborhoods in a graph. In comparison to the works on balls in graphs, we provide improved algorithmic results, notably including FPT algorithms for more general classes of parameters, and we complement these results by deriving stronger lower bounds. Lastly, we obtain combinatorial upper bounds for wider classes of graphs.