ICLR 2026 论文列表

This paper examines the exploration–exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: \textit{spurious rewards}, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and \textit{entropy minimization}, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g., human preferences) before using it to provide *online* feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on said dataset via *offline* maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only *lose* information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a *generation-verification gap*, *(1)* it is relatively easy to learn the relatively simple RM (*verifier*) from the preference data. Then, *(2)* the downstream RL procedure only returns policies (*generators*) that are optimal for such relatively simple verifiers. Thus, end-to-end, two-stage online FT only has to search over a reduced subset of the full space of policies, requiring less data than offline FT.

Multimodal position encoding is essential for vision-language models, yet there has been little systematic investigation into multimodal position encoding. We conduct a comprehensive analysis of multimodal Rotary Positional Embedding (RoPE) by examining its two core components: position design and frequency allocation. Through extensive experiments, we identify three key guidelines: positional coherence, full frequency utilization, and preservation of textual priors—ensuring unambiguous layout, rich representation, and faithful transfer from the pre-trained LLM. Based on these insights, we propose Multi-Head RoPE (MHRoPE) and MRoPE-Interleave (MRoPE-I), two simple and plug-and-play variants that require no architectural changes. Our methods consistently outperform existing approaches across diverse benchmarks, with significant improvements in both general and fine-grained multimodal understanding.

Real-world large language model deployments (e.g., conversational AI systems, code generation assistants) naturally generate abundant implicit user dissatisfaction (DSAT) signals, as users iterate toward better answers through refinements, corrections, and expressed preferences, while explicit satisfaction (SAT) feedback is scarce. Existing preference learning approaches are poorly aligned with this data profile, as they rely on costly human annotations or assume plentiful positive responses. In this paper, we introduce \textbf{DRIFT} (\textbf{D}issatisfaction-\textbf{R}efined \textbf{I}terative pre\textbf{F}erence \textbf{T}raining), which anchors training on real-world DSAT signals and samples positives dynamically from the evolving policy. Empirically, DRIFT models trained on real-world \textit{WildFeedback} datasets and synthetic \textit{UltraFeedback} datasets achieve up to +6.23\% (7B) / +7.61\% (14B) on WildBench Task Score and up to +8.95\% (7B) / +12.29\% (14B) on AlpacaEval2 win rate over base models, outperforming strong baseline methods such as iterative DPO and SPIN. At larger scales, the improvements are particularly pronounced: 14B models trained with DRIFT surpass GPT-4o-mini on WildBench. Further analysis shows that DRIFT also preserves exploratory capacity, yielding more diverse high-reward solutions rather than collapsing to narrow subsets. Theoretically, we demonstrate that this design preserves preference margins and avoids the gradient degeneration. These results show that DRIFT is an effective and scalable recipe for real-world post-training that leverages the most abundant and informative signal.

Real-world settings where language models (LMs) are deployed---in domains spanning healthcare, finance, and other forms of knowledge work—require models to grapple with incomplete information and reason under uncertainty. Yet most LM evaluations focus on problems with well-defined answers and success criteria. This gap exists in part because natural problems involving uncertainty are difficult to construct: given that LMs have access to most of the same knowledge as humans, it is non-trivial to design questions for which LMs will struggle to produce correct answers, but which humans can answer reliably.As a result, LM performance on reasoning under uncertainty remains poorly characterized. To address this gap, we introduce \textsc{OpenEstimate}, an extensible, multi-domain benchmark for evaluating LMs on numerical estimation tasks that require models to synthesize significant amounts of background information and express predictions as probabilistic priors. We assess these priors for accuracy and calibration. Across six frontier models, we find that LM-elicited priors are worth the equivalent of about five samples from the underlying data distribution, and that posteriors computed using LM priors tend to be more accurate than those computed using a naive prior. At the same time, the relationship between model accuracy and confidence is weak across the board, indicating the value of developing new methods to improve calibration. The \textsc{OpenEstimate} benchmark thus offers a challenging evaluation for frontier LMs and a platform for developing models that are better at probabilistic estimation and reasoning under uncertainty.

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.279), which processes the entire proof at once, and step-proof formalization (0.046), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://anonymous.4open.science/r/ProofFlow-351E.

Large Language Models (LLMs) as autonomous agents are increasingly tasked with solving complex, long-horizon problems. Aligning these agents via preference-based methods like Direct Preference Optimization (DPO) is a promising direction, yet it faces a critical granularity mismatch. Trajectory-level DPO provides stable signals but blur where credit should be assigned within long trajectories, whereas step-level DPO offers fine-grained supervision but can be statistically noisy and data-inefficient when Monte Carlo rollouts are limited, and can be hard to fully exploit multi-step structured behaviors that only reveal their effect over several actions. To balance this trade-off, we introduce **H**ierarchical **P**reference **L**earning (HPL), a hierarchical framework that optimizes LLM agents by leveraging preference signals at multiple, synergistic granularities. While HPL incorporates trajectory- and step-level DPO for global and local policy stability, its core innovation lies in group-level preference optimization guided by a dual-layer curriculum. Our approach first decomposes expert trajectories into semantically coherent action groups and then generates contrasting suboptimal groups to enable preference learning at a fine-grained, sub-task level. Then, instead of treating all preference pairs equally, HPL introduces a curriculum scheduler that organizes the learning process from simple to complex. This curriculum is structured along two axes: the group length, representing sub-task complexity, and the sample difficulty, defined by the reward gap between preferred and dispreferred action groups. Experiments on three challenging agent benchmarks show that HPL outperforms existing state-of-the-art methods. Our analyses demonstrate that the hierarchical DPO loss effectively integrates preference signals across multiple granularities, while the dual-layer curriculum is crucial for enabling the agent to solve a wide range of tasks, from simple behaviors to complex multi-step sequences.

Converging evidence suggests that human systems of semantic categories achieve near-optimal compression via the Information Bottleneck (IB) complexity-accuracy tradeoff. Large language models (LLMs) are not trained for this objective, which raises the question: are LLMs capable of evolving efficient human-aligned semantic systems? To address this question, we focus on color categorization --- a key testbed of cognitive theories of categorization with uniquely rich human data --- and replicate with LLMs two influential human studies. First, we conduct an English color-naming study, showing that LLMs vary widely in their complexity and English-alignment, with larger instruction-tuned models achieving better alignment and IB-efficiency. Second, to test whether these LLMs simply mimic patterns in their training data or actually exhibit a human-like inductive bias toward IB-efficiency, we simulate cultural evolution of pseudo color-naming systems in LLMs via a method we refer to as Iterated in-Context Language Learning (IICLL). We find that akin to humans, LLMs iteratively restructure initially random systems towards greater IB-efficiency. However, only a model with strongest in-context capabilities (Gemini 2.0) is able to recapitulate the wide range of near-optimal IB-tradeoffs observed in humans, while other state-of-the-art models converge to low-complexity solutions. These findings demonstrate how human-aligned semantic categories can emerge in LLMs via the same fundamental principle that underlies semantic efficiency in humans.

Electrophysiological (ExG) signals offer valuable insights into human physiology, yet building foundation models that generalize across everyday tasks remains challenging due to two key limitations: (i) insufficient data diversity, as most ExG recordings are collected in controlled labs with bulky, expensive devices; and (ii) task-specific model designs that require tailored processing (i.e., targeted frequency filters) and architectures, which limit generalization across tasks. To address these challenges, we introduce an approach for scalable, task-agnostic ExG monitoring in the wild. We collected 50 hours of unobtrusive free-living ExG data with an earphone-based hardware prototype to narrow the data diversity gap. At the core of our approach is Physiology-informed Multi-band Tokenization (PiMT), which decomposes ExG signals into 12 physiology-informed tokens, followed by a reconstruction task to learn robust representations. This enables adaptive feature recognition across the full frequency spectrum while capturing task-relevant information. Experiments on our new HumanSense dataset, the first to enable ExG-based analysis across five human senses, together with four public ExG benchmarks, demonstrate that PiMT consistently outperforms state-of-the-art methods across diverse tasks.

Neural approaches to the Flexible Job Shop Scheduling Problem (FJSP), particularly those based on deep reinforcement learning (DRL), have gained growing attention in recent years. Yet existing methods often rely on cumbersome state representations (i.e. sometimes requiring more than 20 handcrafted features) and suboptimal neural architectures. We introduce \textsc{ReSched}, a minimalist DRL framework that rethinks both the scheduling formulation and model design. First, we revisit the Markov Decision Process (MDP) formulation of FJSP, reducing the state to just four essential features and replacing historical dependencies with a graph structure that directly encodes intra-job operation relationships. Second, we employ Transformer blocks with dot-product attention, augmented by three lightweight but effective architectural modifications tailored to scheduling. Extensive experiments show that \textsc{ReSched} outperforms classical dispatching rules and state-of-the-art DRL methods on FJSP. Moreover, \textsc{ReSched} generalizes well to the Job Shop Scheduling Problem (JSSP) and the Flexible Flow Shop Scheduling Problem (FFSP), achieving competitive performance against neural baselines specifically designed for these variants.

Incorporating robustness in generative modeling has enticed many researchers of the field. To this end, we introduce a new class of multivariate power-law distributions---the symmetric Pareto (symPareto) distribution---which can be viewed as an $\ell_1$-norm-based counterpart of the multivariate $t$ distribution. The symPareto distribution possesses many attractive information-geometric properties with respect to the $\gamma$-power divergence that naturally populates power-law families. Leveraging on the joint minimization view of variational inference, we propose the ParetoVAE, a probabilistic autoencoder that minimizes the $\gamma$-power divergence between two statistical manifolds. ParetoVAE employs the symPareto distribution for both prior and encoder, with flexible decoder options including Student's $t$ and symPareto distributions. Empirical evidences demonstrate ParetoVAE's effectiveness across multiple domains through varying the types of the decoder. The $t$ decoder achieves superior performance in sparse, heavy-tailed data reconstruction and word frequency analysis; the symPareto decoder enables robust high-dimensional denoising.

Time series forecasting is of significant importance across various domains. However, it faces significant challenges due to distribution shift. This issue becomes particularly pronounced in online deployment scenarios where data arrives sequentially, requiring models to adapt continually to evolving patterns. Current time series online learning methods focus on two main aspects: selecting suitable parameters to update (e.g., final layer weights or adapter modules) and devising suitable update strategies (e.g., using recent batches, replay buffers, or averaged gradients). We challenge the conventional parameter selection approach, proposing that distribution shifts stem from changes in underlying latent factors influencing the data. Consequently, updating the feature representations of these latent factors may be more effective. To address the critical problem of delayed feedback in multi-step forecasting (where true values arrive much later than predictions), we introduce ADAPT-Z (Automatic Delta Adjustment via Persistent Tracking in Z-space). ADAPT-Z utilizes an adapter module that leverages current feature representations combined with historical gradient information to enable robust parameter updates despite the delay. Extensive experiments demonstrate that our method consistently outperforms standard base models without adaptation and surpasses state-of-the-art online learning approaches across multiple datasets.

Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, or visual understanding. Generating such graphs enables simulation, data augmentation and novel instance discovery; however, this task remains underexplored. We identify two key reasons: first, modeling edge directionality introduces a substantially larger dependency space, making the underlying distribution harder to learn; second, the absence of standardized benchmarks hinders rigorous evaluation. Addressing the former limitation requires more expressive models that are sensitive to directional topologies. Thus, we propose Directo, the first generative model for directed graphs built upon the discrete flow matching framework. Our approach combines: (i) a dual-attention mechanism distinctly capturing incoming and outgoing dependencies, (ii) a robust, discrete generative framework, and (iii) principled positional encodings tailored to asymmetric pairwise relations. To address the second limitation and support evaluation, we introduce a novel and extensive benchmark suite covering synthetic and real-world datasets. Experiments show that our method outperforms existing directed graph generation approaches across diverse settings and competes with specialized models for particular classes, such as directed acyclic graphs. These results highlight the effectiveness and generality of our approach, establishing a solid foundation for future research in directed graph generation.

Ensemble learning is a practical family of methods for uncertainty modeling, particularly useful for sequential decision-making problems like recommendation systems and reinforcement learning tasks. The posterior on likelihood parameters is approximated by sampling an ensemble member from a predetermined index distribution, with the ensemble’s diversity reflecting the degree of uncertainty. In this paper, we propose Bayesian Ensemble (BE), a lightweight yet principled Bayesian layer atop existing ensembles. BE treats the selection of an ensemble member as a bandit problem in itself, dynamically updating a sampling distribution over members via Bayesian inference on observed rewards. This contrasts with prior works that rely on fixed, uniform sampling. We extend this framework to both bandit learning and reinforcement learning, introducing Bayesian Ensemble Bandit and Bayesian Ensemble Deep Q-Network for diverse decision-making problems. Extensive experiments on both synthetic and real-world environments demonstrate the effectiveness and efficiency of BE.

Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations untapped. Inspired by the recent success of vision-language pre-training, this paper enriches the landscape of spectral clustering from a single-modal to a multi-modal regime. Particularly, we propose Neural Tangent Kernel Spectral Clustering that leverages cross-modal alignment in pre-trained vision-language models. By anchoring the neural tangent kernel with positive nouns, i.e., those semantically close to the images of interest, we arrive at formulating the affinity between images as a coupling of their visual proximity and semantic overlap. We show that this formulation amplifies within-cluster connections while suppressing spurious ones across clusters, hence encouraging block-diagonal structures. In addition, we present a regularized affinity diffusion mechanism that adaptively ensembles affinity matrices induced by different prompts. Extensive experiments on \textbf{16} benchmarks---including classical, large-scale, fine-grained and domain-shifted datasets---manifest that our method consistently outperforms the state-of-the-art by a large margin.

Visual Autoregressive (VAR) models enhance generation speed but face a critical efficiency bottleneck in later stages. In this paper, we present a novel optimization framework for VAR models that fundamentally differs from prior approaches such as FastVAR and SkipVAR. Instead of relying on heuristic skipping strategies, our method leverages attention entropy to characterize the semantic projections across different dimensions of the model architecture. This enables precise identification of parameter dynamics under varying token granularity levels, semantic scopes, and generation scales. Building on this analysis, we further uncover sparsity patterns along three critical dimensions—token, layer, and scale—and propose a set of fine-grained optimization strategies tailored to these patterns. Extensive evaluation demonstrates that our approach achieves aggressive acceleration of the generation process while significantly preserving semantic fidelity and fine details, outperforming traditional methods in both efficiency and quality. Experiments on Infinity-2B and Infinity-8B models demonstrate that ToProVAR achieves nearly 3.5× average acceleration with minimal quality loss, effectively mitigating the issues found in prior work. Our code will be made publicly available.

As large language models expand beyond natural language to domains such as mathematics, multimodal understanding, and embodied agents, tokens increasingly reflect metric relationships rather than purely linguistic meaning. We introduce DIST2Loss, a distance-aware framework designed to train autoregressive discrete models by leveraging predefined distance relationships among output tokens. At its core, DIST2Loss transforms continuous exponential family distributions derived from inherent distance metrics into discrete, categorical optimization targets compatible with the models’ architectures. This approach enables the models to learn and preserve meaningful distance relationships during token generation while maintaining compatibility with existing architectures. Empirical evaluations show consistent performance gains in diverse multimodal applications, including visual grounding, robotic manipulation, generative reward modeling, and image generation using vector-quantized features. These improvements are most notable in low-data regimes, demonstrating DIST2Loss’s strength under resource constraints.

Learning causal structures from temporal data is fundamental to many practical tasks, such as physical laws discovery and root causes localization. Real-world systems often exhibit long-term carry-over effects, where the value of a variable at the current time can be influenced by distant past values of other variables. These effects, due to their large temporal span, are challenging to observe or model. Existing methods typically consider finite lag orders, which may lead to confounding from early historical data. Moreover, incorporating historical information often results in computational scalability issues. In this paper, we establish a theoretical framework for causal discovery in complex temporal scenarios where observational data exhibit long-term carry-over effect, and propose LEVER, a theoretically guaranteed novel causal discovery method for incomplete temporal data. Specifically, based on the \textit{Limited-history Causal Identifiability Theorem}, we refine the variable values at each time step with data at a few preceding steps to mitigate long-term historical influences. Furthermore, we establish a theoretical connection between QR decomposition and causal discovery, and design an efficient reinforcement learning process to determine the optimal variable ordering. Finally, we recover the causal structure from the R matrix. We evaluate LEVER on both synthetic and real-world datasets. In static cases, LEVER reduces SHD by 17.29\%-40.00\% and improves the F1-score by 5.30\%-8.79\% compared to the best baseline. In temporal cases, it achieves a 64\% reduction in SHD and a 45\% improvement in F1-score. Additionally, LEVER demonstrates significantly higher precision on real-world data compared to baseline methods.

Although reinforcement learning (RL) can effectively enhance the reasoning capabilities of vision–language models (VLMs), current methods remain heavily dependent on labor-intensive datasets that require extensive manual construction and verification, leading to extremely high training costs and consequently constraining the practical deployment of VLMs. To address this challenge, we propose **Vision-Zero**, *a domain-agnostic self-play framework that generates visual deduction games from diverse images for scalable VLM training without human annotations.* Specifically, Vision-Zero encompasses three main attributes: (1) **Strategic Self-Play Framework:** Vision-Zero trains VLMs in "Who Is the Spy"-style games, where the models engage in strategic reasoning and actions across multiple roles. Through interactive gameplay, models autonomously generate their training data without human annotation. (2) **Gameplay from Arbitrary Images:** Unlike existing gamified frameworks, Vision-Zero can generate games from arbitrary images, thereby enhancing the model’s reasoning ability across diverse domains and showing strong generalization to different tasks. We demonstrate this versatility using three distinct types of image datasets: CLEVR-based synthetic scenes, charts, and real-world images. (3) **Sustainable Performance Gain:** We introduce Iterative Self-Play Policy Optimization (Iterative-SPO), a novel training algorithm that alternates between Self-Play and reinforcement learning with verifiable rewards (RLVR), mitigating the performance plateau often seen in self-play-only training and achieving sustained long-term improvements. Despite using label-free data, Vision-Zero achieves state-of-the-art performance on reasoning, chart question answering, and vision-centric understanding tasks, surpassing other annotation-based methods. Models and code will be released upon acceptance.