ICLR 2026 Papers

In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While expensive to create, such a dataset is essential for driving improvements in training and addressing key open questions in the field of automated proof generation. Specifically, it remains unknown (1) how large the gap is between natural language and formal proof generation, (2) how final-answer accuracy relates to full proof correctness, and (3) how best-of-n selection strategies can affect proof quality. In this work, we present the Open Proof Corpus (OPC), a dataset comprising over 5,000 human-evaluated proofs produced by state-of-the-art LLMs. The OPC was specifically designed for broad applicability and downstream usage in proof generation research and is the first large dataset of LLM-generated solutions to problems from prestigious mathematics competitions such as the USAMO and IMO. Using the OPC, we address the open questions outlined above and provide new insights into LLMs' strengths and limitations in mathematical reasoning. Finally, to showcase the utility of the OPC, we finetune an 8B-parameter model on the dataset, obtaining a model that matches Gemini-2.5-Pro, and performs close to the best model, GPT-5, on evaluating proof correctness.

Long-sequence processing is a critical capability for modern large language models. However, the self-attention mechanism in the standard Transformer architecture faces severe computational and memory bottlenecks when processing long sequences. While trainable sparse attention methods offer a promising solution, existing approaches such as NSA introduce excessive extra parameters and disrupt the conventional pretrain-on-short, finetune-on-long workflow, resulting in slow convergence and difficulty in acceleration. To overcome these limitations, we introduce Dense-Sparse Switchable Attention framework (DSSA), a trainable sparse attention that seamlessly adapts models from short to long sequences. Specifically, DSSA reuses dense attention parameters through parameter-free architecture modification, maintaining consistency between short and long sequence processing. Additionally, DSSA ensures computational efficiency across all sequence lengths, by using dense attention for short inputs and smoothly transitioning to sparse attention for long sequences. To achieve practical acceleration, we further introduce an efficient implementation of DSSA that significantly reduces the computational overhead. Our experiments on long-context understanding and chain-of-thought reasoning demonstrate that DSSA is $4\times$ faster than dense attention while retaining 98.1% and 99.7% of the performance, respectively. We will release all associated implementations to facilitate future research on efficient attention.

While Long Chain-of-Thought (CoT) reasoning significantly improves Large Language Models (LLMs) performance on complex reasoning tasks, the substantial computational and memory costs of generating long CoT sequences limit their efficiency and practicality. Existing studies usually enhance the reasoning efficiency of LLMs by compressing CoT sequences. However, this approach conflicts with test‑time scaling, limiting the reasoning capacity of LLMs. In this paper, we propose an efficient reasoning framework that models the reasoning process of LLMs as a state‑transition process. Specifically, we first apply a linear attention mechanism to estimate the LLM’s reasoning state, which records the historical reasoning information from previous reasoning steps. Then, based on the query prompt and the reasoning state, the LLM can efficiently perform the current reasoning step and update the state. With the linear attention, each token in the current reasoning step can directly retrieve relevant historical reasoning information from the reasoning state, without explicitly attending to tokens in previous reasoning steps. In this way, the computational complexity of attention is reduced from quadratic to linear, significantly improving the reasoning efficiency of LLMs. In addition, we propose a state-based reasoning strategy to mitigate the over-thinking issue caused by noisy reasoning steps. Extensive experiments across multiple datasets and model sizes demonstrate that our framework not only improves the reasoning efficiency of LLMs but also enhances their reasoning performance.

Reasoning has emerged as a key capability of large language models. In linguistic tasks, this capability can be enhanced by self-improving techniques that refine reasoning paths for subsequent fine-tuning. However, extending these language-based self-improving approaches to vision language models (VLMs) presents a unique challenge: visual hallucinations in reasoning paths cannot be effectively verified or rectified. Our solution starts with a key observation about visual contrast: when presented with a contrastive VQA pair, i.e., two visually similar images with synonymous questions, VLMs identify relevant visual cues more precisely compared with when given a single VQA sample. Motivated by this observation, we propose Visual Contrastive Self-Taught Reasoner (VC-STaR), a novel self-improving framework that leverages visual contrast to mitigate hallucinations in model-generated rationales. We collect a diverse suite of VQA datasets, curate contrastive pairs according to multi-modal similarity, and generate rationales using VC-STaR. Consequently, we obtain a new visual reasoning dataset, VisCoR-$55$K, which is then used to boost the reasoning capability of various VLMs through supervised finetuning. Extensive experiments show that VC-STaR not only outperforms existing self-improving approaches but also surpasses models finetuned on the SoTA visual reasoning datasets, demonstrating that the inherent contrastive ability of VLMs can bootstrap their own visual reasoning. The code, dataset and trained models will be released upon acceptance.

Estimating potential outcomes for treatments over time based on observational data is important for personalized decision-making in medicine. However, many existing methods for this task fail to properly adjust for time-varying confounding and thus yield biased estimates. There are only a few neural methods with proper adjustments, but these have inherent limitations (e.g., division by propensity scores that are often close to zero), which result in poor performance. As a remedy, we introduce the iterative G-computation network (IGC-Net). Our IGC-Net is a novel, neural end-to-end model which adjusts for time-varying confounding in order to estimate conditional average potential outcomes (CAPOs) over time. Specifically, our IGC-Net is the first neural model to perform fully regression-based iterative G-computation for CAPOs in the time-varying setting. We evaluate the effectiveness of our IGC-Net across various experiments. In sum, this work represents a significant step towards personalized decision-making from electronic health records.

The reliability of Large Language Models (LLMs) in high-stakes domains such as healthcare, law, and scientific discovery is often compromised by hallucinations. These failures typically stem from two sources: *data-driven hallucinations* and *reasoning-driven hallucinations*. However, existing detection methods usually address only one source and rely on task-specific heuristics, limiting their generalization to complex scenarios. To overcome these limitations, we introduce the *Hallucination Risk Bound*, a unified theoretical framework that formally decomposes hallucination risk into data-driven and reasoning-driven components, linked respectively to training-time mismatches and inference-time instabilities. This provides a principled foundation for analyzing how hallucinations emerge and evolve. Building on this foundation, we introduce **HalluGuard**, an NTK-based score that leverages the induced geometry and captured representations of the NTK to jointly identify data-driven and reasoning-driven hallucinations. We evaluate **HalluGuard** on 10 diverse benchmarks, 11 competitive baselines, and 9 popular LLM backbones, consistently achieving state-of-the-art performance in detecting diverse forms of LLM hallucinations.

Despite the empirical success of extensive, step-by-step reasoning in large multimodal models, long reasoning processes inevitably incur substantial computational overhead, i.e., in terms of higher token costs and increased response time, which undermines inference efficiency. In contrast, humans often employ sketch-style reasoning: a concise, goal-directed cognitive process that prioritizes salient information and enables efficient problem-solving. Inspired by this cognitive efficiency, we propose SketchThinker-R1, which incentivizes sketch-style reasoning ability in large multimodal models. Our method consists of three primary stages. In the Sketch-Mode Cold Start stage, we convert standard long reasoning process into sketch-style reasoning and finetune base multimodal model, instilling initial sketch-style reasoning capability. Next, we train SketchJudge Reward Model, which explicitly evaluates thinking process of model and assigns higher scores to sketch-style reasoning. Finally, we conduct Sketch-Thinking Reinforcement Learning under supervision of SketchJudge to further generalize sketch-style reasoning ability. Experimental evaluation on four benchmarks reveals that our SketchThinker-R1 achieves over 64% reduction in reasoning token cost without compromising final answer accuracy. Qualitative analysis further shows that sketch-style reasoning focuses more on key cues during problem solving.

Intelligent systems must form internal representations that support both broad generalization and precise identification. Here, we show that these two goals are fundamentally in tension with one another. We derive closed-form expressions proving that any model whose representations have a finite semantic resolution, impairing long-range similarity computations, must lie on a universal Pareto front linking its probability of correct generalization $p_S$ and identification $p_I$. We extend this analysis to general input spaces and to parallel processing scenarios, predicting a sharp $1/n$ collapse in the capacity of processing multiple inputs at the same time. A minimal ReLU network reproduces these laws: a resolution boundary emerges during learning, and empirical $(p_S,p_I)$ trajectories closely match the theory for linearly decaying similarity. Finally, we show that the same limits appear in far more complex systems, including a convolutional neural network and state-of-the-art vision–language models, indicating that learned finite-resolution similarity are broad and foundational informational constraints rather than toy-model artifacts. Together, these results provide a precise theory of the generalization–identification tradeoff and clarify how semantic resolution shapes the representational capacity of deep networks and brains alike.

Inference-time computation, analogous to human System 2 Thinking, has recently become popular for improving model performance. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question “Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?” We find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs)---a new class of Energy-Based Models (EBMs)---to assign an energy value to every input and candidate-prediction, enabling predictions through energy minimization until convergence. To support this approach, we introduce several key techniques for stable and parallelizable training, which enable the emergence of strong System 2 Thinking capabilities and scalable EBMs. Across discrete and continuous modalities, we find EBTs outperform the Transformer++ approach, scaling up to 35% faster during pretraining, and improving inference-time performance by up to 29%. EBTs also surpass Diffusion Transformers on image denoising while requiring 99% fewer forward passes. Moreover, System 2 Thinking with EBTs yields larger performance gains on data that is farther out-of-distribution, and EBTs achieve better results than existing models on most downstream tasks despite achieving the same or worse pretraining performance, enabling EBTs to generalize better than existing approaches. Consequently, EBTs are a flexible and exciting new approach for scaling both the learning and thinking capabilities of models.

Personalized alignment is crucial for enabling Large Language Models (LLMs) to engage effectively in user-centric interactions. However, current methods face a dual challenge: they fail to infer users' deep implicit preferences (including unstated goals, semantic context and risk tolerances), and they lack the defensive reasoning required to navigate real-world ambiguity. This cognitive gap leads to responses that are superficial, brittle and short-sighted. To address this, we propose Critique-Driven Reasoning Alignment (CDRA), which reframes alignment from a scalar reward-matching task into a structured reasoning process. First, to bridge the preference inference gap, we introduce the DeepPref benchmark. This dataset, comprising 3000 preference-query pairs across 20 topics, is curated by simulating a multi-faceted cognitive council that produces critique-annotated reasoning chains to deconstruct query semantics and reveal latent risks. Second, to instill defensive reasoning, we introduce the Personalized Generative Process Reward Model (Pers-GenPRM), which frames reward modeling as a personalized reasoning task. It generates a critique chain to evaluate a response's alignment with user preferences before outputting a final score based on this rationale. Ultimately, this interpretable, structured reward signal guides policy model through Critique-Driven Policy Alignment, a process-level online reinforcement learning algorithm integrating both numerical and natural language feedback. Experiments demonstrate that CDRA excels at discovering and aligning with users' true preferences while executing robust reasoning. Our code and dataset are available at https://anonymous.4open.science/r/Deep-pref-9DE9.

Visual generation models have made remarkable progress in creating realistic images from text prompts, yet struggle with complex prompts that specify multiple objects with precise spatial relationships and attributes. Effective handling of such prompts requires explicit reasoning about the semantic content and spatial layout. We present GoT-R1, a framework that applies reinforcement learning to enhance semantic-spatial reasoning in autoregressive visual generation models. Leveraging the natural affinity between autoregressive architectures and sequential reasoning, our approach builds upon the Generation Chain-of-Thought framework to enable models to autonomously discover effective reasoning strategies beyond predefined templates. To achieve this, we propose a dual-stage multi-dimensional reward framework that leverages MLLMs to evaluate both the reasoning process and final output, enabling effective supervision across the entire generation pipeline. The reward system assesses semantic alignment, spatial accuracy, and visual quality in a unified approach. Experimental results demonstrate significant improvements on T2I-CompBench and GenEval benchmark, particularly in compositional tasks involving precise spatial relationships and attribute binding. GoT-R1 advances the state-of-the-art in autoregressive image generation by successfully transferring sophisticated reasoning capabilities from language models to the visual generation domain. Code is available at https://github.com/gogoduan/GoT-R1.

Tables serve as a fundamental format for representing structured relational data. While current language models (LMs) excel at many text-based tasks, they still face challenges in table understanding due to the complex characteristics of tabular data, such as their structured nature. In this paper, we aim to enhance LMs for improved table understanding. We identify four key challenges: 1) difficulty in locating target data, 2) deficiency in table semantics, 3) numerical inaccuracies in textual reasoning, and 4) semantic inflexibility in symbolic reasoning. To address these issues, we propose TableMaster, a recipe and comprehensive framework that integrates multiple solutions to overcome these obstacles. TableMaster first extracts relevant table content and verbalizes it with enriched semantic context. Additionally, we introduce adaptive reasoning, a flexible approach that dynamically adjusts between textual and symbolic reasoning, tailoring the reasoning process to each query. Extensive analyses and experiments demonstrate our findings and the effectiveness of TableMaster. On the WikiTQ dataset, TableMaster achieves an accuracy of 78.13% using GPT-4o-mini, surpassing existing baselines. We hope this work will serve as a practical step toward more robust and reliable table understanding.

Reasoning models improve their problem-solving ability through inference-time scaling, allocating more compute via longer token budgets. Identifying which reasoning traces are likely to succeed remains a key opportunity: reliably predicting productive paths can substantially reduce wasted computation and improve overall efficiency. We introduce Latent-Trajectory signals that characterize the temporal evolution of a model's internal representations during the generation of intermediate reasoning tokens. By analyzing both the extent and temporal course of latent representational change, as well as its alignment with the final state, we show that these signals are strong predictors of solution accuracy, outperforming conventional output-based confidence measures. We use latent-trajectory signals to guide answer selection across multiple sampled generations, demonstrating that they make test-time scaling more effective and efficient, reducing token usage by up to 70% while preserving and even improving accuracy by 2.6% on average in comparison with majority voting. Finally, we show that these signals often emerge early in the reasoning trace, which enables early selection and allocation of compute to the most promising candidates during generation. Our findings contribute not only practical strategies for inference-time efficiency, but also a deeper interpretability perspective on how reasoning processes are represented and differentiated in latent space.

Multimodal Large Language Models (MLLMs) suffer from hallucinations. Existing hallucination evaluation benchmarks are often limited by over-simplified tasks leading to saturated metrics, or insufficient diversity that fails to adequately assess the hallucination extent in state-of-the-art multimodal models. To address this gap, we propose FREAK, a comprehensive multimodal benchmark designed for fine-grained hallucination assessment in MLLMs. Through high-quality photorealistic images featuring fine-grained counter-commonsense edits, FREAK innovatively evaluates hallucination phenomena in detailed visual perception of MLLMs. Extensive experiments on FREAK show severe hallucination issues in SOTA models regarding detailed visual perception. To enable deeper investigation, we curate a controlled subset to indirectly evaluate the model’s ability to perceive target detailed information. Through systematic evaluation of prevailing Chain-of-Thought (CoT) prompting techniques within this task, we reveal critical insights regarding hallucination patterns and model reasoning processes.

Large language models (LLMs) benefit from test-time scaling but are often hampered by high inference latency. Speculative decoding is a natural way to accelerate the scaling process; however, scaling along both the parallel and sequential dimensions poses significant challenges, including substantial memory-bound execution and synchronization overhead. We introduce *ATTS* (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive scaling framework that follows the hypothesis testing process to address these challenges. By revisiting arithmetic intensity, *ATTS* identifies synchronization as the primary bottleneck. It enables asynchronous inference through online calibration and proposes an ordinal classification algorithm that supports a three-stage rejection sampling pipeline, scaling along both the sequential and parallel axes. Across experiments on the MATH, AMC23, AIME24, and AIME25 datasets and across multiple draft–target model families, we show that *ATTS* delivers up to *56.7x* speedup in test-time scaling and a *4.14x* throughput improvement, while maintaining accurate control of the rejection rate, reducing latency and memory overhead, and incurring no accuracy loss. By scaling both in parallel and sequential dimensions, we enable the 1.5B/70B draft/target model combination to achieve the performance of the state-of-the-art reasoning model o3-mini (high) on the AIME dataset. We submit the anonymous repository: anonymous.4open.science/r/Asynchronous-Test-Time-Scaling-5940.

Current speech-language models (SLMs) typically use a cascade of speech encoder and large language model, treating speech understanding as a single black box. They analyze the content of speech well but reason weakly about other aspects, especially under sparse supervision. Thus, we argue for explicit reasoning over speech states and actions with modular and transparent decisions. Inspired by cognitive science we adopt a modular perspective and a world model view in which the system learns forward dynamics over latent states. We factorize speech understanding into four modules that communicate through a causal graph, establishing a cognitive state search space. Guided by posterior traces from this space, an instruction-tuned language model produces a concise causal analysis and a user-facing response, enabling counterfactual interventions and interpretability under partial supervision. We present the first graph based modular speech model for explicit reasoning and we will open source the model and data to promote the development of advanced speech understanding.

Reinforcement learning (RL) training of large language models (LLMs) is limited by the policy's ability to generate rollouts with non-zero rewards: without such rewards, the policy is not updated and learning is stalled on hard problems, which are problems that the policy consistently fails to sample any correct rollouts for. We find that many hard problems remain unsolved due to the repeated generation of incorrect intermediate steps in a long reasoning trace; identifying and fixing these requires performing better \emph{credit assignment}. But existing approaches for credit assignment are either impractical or impose a substantial data-writing burden on oracles (\textit{e.g.}, humans). In this paper, we introduce \textbf{Interventional Training} (InT), a framework that leverages single-step oracle interventions to improve LLM reasoning. Given a reasoning attempt and ground-truth answer, the oracle detects and then provides language feedback on a single intermediate reasoning step, which is much cheaper than obtaining a full reasoning trace. \methodname{} then \emph{patches} the LLM by running supervised fine-tuning on the on-policy rollout up to the error, followed by the correction from the oracle. RL on this patched model now generates counterfactual traces and with merely $\approx$$100$ interventions from the oracle, \methodname{} solves 16\% more hard test problems that were previously unsolved (only zero rewards) and also improves performance across multiple standard evals.

Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into additional steps, backtracking, and correcting mistakes. Despite its strong performance--demonstrated by OpenAI's o1 and DeepSeek R1, the conditions in the training data under which long CoTs emerge, and when such long CoTs improve the performance, remain unclear. In this paper, we study the performance of test-time scaling for transformers trained on an in-context weight prediction task for linear regression. Our analysis provides a theoretical explanation for several intriguing observations: First, at any fixed test error, increasing test-time compute allows us to reduce the number of in-context examples (context length) in training prompts. Second, if the skills required to solve a downstream task are not sufficiently present in the training data, increasing test-time compute can harm performance. Finally, we characterize task hardness via the smallest eigenvalue of its feature covariance matrix and show that training on a diverse, relevant, and hard set of tasks results in best performance for test-time scaling. We confirm our findings with experiments on large, nonlinear transformer architectures.

LLM-based reasoning models have enabled the development of agentic systems that act as co-scientists, assisting in multi-step scientific analysis. However, evaluating these systems is challenging, as it requires realistic, end-to-end research scenarios that integrate data analysis, interpretation, and the generation of new insights from the experimental data. To address this limitation, we introduce HeurekaBench, a framework to create benchmarks with *exploratory, open-ended research questions* for experimental datasets. Each such question is grounded in a scientific study and its corresponding code repository, and is created using a semi-automated pipeline that leverages multiple LLMs to extract insights and generate candidate workflows, which are then verified against reported findings. We instantiate the framework in single-cell biology to obtain sc-HeurekaBench benchmark and use it to compare state-of-the-art single-cell agents. We further showcase the benefits of our benchmark for quantitatively analyzing current design choices in agentic systems. We find that the addition of a *critic* module can improve ill-formed responses for open-source LLM-based agents by up to 22% and close the gap with their closed-source counterparts. Overall, HeurekaBench sets a path toward rigorous, end-to-end evaluation of scientific agents, grounding benchmark construction in real scientific workflows.