ICLR 2026 Papers

Large language models, constrained by the fixed-depth Transformer architecture, struggle to solve complex reasoning tasks in an end-to-end manner. Existing approaches, such as Chain of Thought, improve reasoning depth to some extent but rely heavily on natural language generation, with computational costs increasing rapidly as the length of the generated sequence grows. To address these limitations, we propose ChainGPT, a dual-reasoning model that shifts reasoning into latent computational space. Within each layer, ChainGPT employs multi-substep state updates combined with state-guided sparse attention, enabling deep local computation and efficient long-range modeling without quadratic costs. Across layers, recurrent depth approach iteratively refine latent states, supported by adaptive training and stopping strategies that balance reasoning depth against computational budget. Theoretically, we show that ChainGPT can, in principle, simulate general computation, and empirically it delivers consistent improvements over comparable models, including on reasoning tasks that remain challenging for existing systems. By unifying efficiency and reasoning ability, ChainGPT provides a principled foundation for next-generation language models.

Learning instantaneous and time-lagged causal relationships from time-series data is essential for uncovering fine-grained, temporally-aware interactions. Although this problem has been formulated as a continuous optimization task amenable to modern machine learning methods, existing approaches largely neglect the use of coarse-grained, lag-agnostic causal priors, an important form of prior knowledge that is often available in practice. To address this gap, we propose a novel framework for structure learning from time series to integrate lag-agnostic priors, enabling the discovery of lag-specific causal links without requiring precise temporal annotations. We introduce formulations to precisely characterize the lag-agnostic prior, and demonstrate their consequential and process-equivalence to priors, maintaining consistency with the intended semantics of the priors throughout optimization. We further analyze the challenge for optimization due to the increased non-convexity by lag-agnostic prior constraints, and introduce a data-driven initialization to mitigate this issue. Experiments on both synthetic and real-world datasets show that our method effectively incorporates lag-agnostic prior knowledge to enhance the recovery of fine-grained, lag-aware structures.

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model’s confidence. Additionally, it yields $4.9\\%$ higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C‑voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme ($95.2\\%$ vs. $55.0\\%$) and Maze ($78.6\\%$ vs. $74.5\\%$) tasks.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

In the field of multimodal chain-of-thought (CoT) reasoning, existing approaches predominantly rely on reasoning on pure linguistic space, which inherently suffers from language bias and is largely confined to math or science domains. This narrow focus limits their ability to handle complex visual reasoning tasks that demand comprehensive understanding of image details. To address these limitations, this paper introduces VGR, a novel reasoning multimodal large language model (MLLM) that can replay the visual memory during thinking just like humans. Unlike traditional MLLMs, VGR first thinks the question and detects relevant regions that may help solve problems, then, the visual memory from the critical area is extracted to assist reasoning. To achieve this, we curate a large-scale SFT dataset called VGR-SFT that contains reasoning data with mixed vision grounding and language deduction. This teaches VGR to think and actively choose grounding areas for key information before answering, and we propose a dynamic visual memory replay stage to integrates the corresponding information into the reasoning process, enhancing multimodel comprehension. Experiments on the LLaVA-NeXT-7B baseline show that VGR achieves superior performance on multimodal benchmarks requiring comprehensive image detail understanding. Compared to the baseline, VGR uses only 30% of the image token count while delivering scores of +4.1 on MMStar, +7.1 on AI2D, and +12.9 improvement on ChartQA.

Does reinforcement learning (RL) teach large language models (LLMs) genuinely new skills, or does it merely activate existing ones? This question lies at the core of ongoing debates about the role of RL in LLM post-training. On one side, strong empirical results can be achieved with RL alone even without preceding supervised finetuning; on the other, critics argue that RL contributes little beyond reweighting existing reasoning strategies. This work provides concrete evidence that LLMs can acquire genuinely new skills during RL by composing existing ones, mirroring one of the central mechanisms by which humans acquire new cognitive skills \citep{Anderson1982Acquisition}. To mitigate data contamination and other confounding factors and to allow precise control over task complexity, we develop a synthetic framework for our investigation. Specifically, we define a skill as the ability to infer the output of a string transformation function $f(x)$ given $x$. Once an LLM has already learned $f$ and $g$ prior to RL, our experiments reveal that RL enables it to learn unseen compositions of them $h(x)=g(f(x))$. Further, this compositional ability generalizes to more difficult problems such as compositions of $>2$ functions unseen during training. Our experiments provide surprising evidence that this compositional ability, acquired on the source task, transfers to a different target task. This transfer occurs even though the model has never trained with RL on any compositional problems in the target task, as long as it has acquired the target task's atomic skills prior to RL on the source task. Our qualitative analysis shows that RL fundamentally changes the reasoning behaviors of the models. In contrast, neither of the findings is observed in next-token prediction training with the same data. Our systematic experiments provide fresh insights into the learning behaviors of widely-used post-training approaches for LLMs. They suggest the value of building base models with the necessary basic skills, followed by RL with appropriate incentivization to acquire more advanced skills that generalize better to complex and out-of-domain problems.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design Calibrated Test-Time Scaling (CaTS), adapting common repeated sampling methods, such as self-consistency and Best-of-N to handle queries of various difficulty. We also show that CaTS-SC is provably better than vanilla self-consistency. Experiments on three LLMs across nine datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping (CaTS-ES) to Best-of-N improves MathQA accuracy from 73.7 to 83.6 with a sample budget of 16 responses, demonstrating the effectiveness of the confidence-based sampling strategy at inference time.

Reasoning about failures is crucial for building reliable and trustworthy robotic systems. Prior approaches either treat failure reasoning as a closed-set classification problem or assume access to ample human annotations. Failures in the real world are typically subtle, combinatorial, and difficult to enumerate, whereas rich reasoning labels are expensive to acquire. We address this problem by introducing ARMOR: Adaptive Round-based Multi-task mOdel for Robotic failure detection and reasoning. We formulate detection and reasoning as a multi-task self-refinement process, where the model iteratively predicts detection outcomes and natural language reasoning conditioned on past outputs. During training, ARMOR learns from heterogeneous supervision - large-scale sparse binary labels and small-scale rich reasoning annotations - optimized via a combination of offline and online imitation learning. At inference time, ARMOR generates multiple refinement trajectories and selects the most confident prediction via a self-certainty metric. Experiments across diverse environments show that ARMOR achieves state-of-the-art performance by improving over the previous approaches by up to 30\% on failure detection rate and up to 100\% in reasoning measured through LLM fuzzy match score, demonstrating robustness to heterogeneous supervision and open-ended reasoning beyond predefined failure modes. We provide dditional visualizations on our website: https://sites.google.com/utexas.edu/armor.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, but their high computational costs limit their widespread practical application. We argue that this inefficiency arises from the tight coupling of high-level cognitive planning (devising the solution strategy) and low-level linguistic realization (generating step-by-step text). To address this challenge, we propose a novel collaborative framework that decouples these two processes through Latent Guidance. Our approach implements a division of labor: a large model acts as an Implicit Thinker, performing high-level cognitive planning and compressing its solution strategy into a set of compact latent guidance vectors. A small, efficient model then serves as an Explicit Executor, which receives this latent guidance to generate a concise and effective reasoning chain. This process is enabled by a dual-loss training objective, grounded in information-theoretic principles, where a reconstruction loss explicitly compels the latent guidance to become a high-fidelity representation of the full reasoning chain. Extensive experiments on 8 diverse reasoning benchmarks demonstrate that our method substantially enhances the reasoning capabilities of small models across various scales (from 0.5B to 8B), allowing them to outperform strong baselines and exhibit superior generalization. Notably, our framework boosts small model accuracy by up to 13.9% and its speed by 2x over its standalone baseline, while being up to 4x faster than the large model. Our work introduces a new, theoretically-grounded paradigm for empowering small models with large-model thinking, substantially improving the performance-cost trade-off for complex reasoning.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose **F**lawed-**A**ware **P**olicy **O**ptimization (**FAPO**), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

Vision-language models (VLMs) are essential to Embodied AI, enabling robots to perceive, reason, and act in complex environments. They also serve as the foundation for the recent Vision-Language-Action (VLA) models. Yet, most evaluations of VLMs focus on single-view settings, leaving their ability to integrate multi-view information largely underexplored. At the same time, multi-camera setups are increasingly standard in robotic platforms, as they provide complementary perspectives to mitigate occlusion and depth ambiguity. Whether VLMs can effectively leverage such multi-view inputs for robotic reasoning therefore remains an open question. To bridge this gap, we introduce MV-RoboBench, a benchmark specifically designed to evaluate the multi-view spatial reasoning capabilities of VLMs in robotic manipulation. MV-RoboBench consists of 1.7k manually curated QA items across eight subtasks, divided into two primary categories: spatial understanding and robotic execution. We evaluate a diverse set of existing VLMs, including both open-source and closed-source models, along with enhanced versions augmented by Chain-of-Thought (CoT)-inspired enhancements. The results show that state-of-the-art models remain far below human performance, underscoring the substantial challenges VLMs face in multi-view robotic perception. Additionally, our analysis uncovers two key findings: (i) spatial intelligence and robotic task reasoning are correlated in multi-view robotic scenarios; and (ii) strong performance on existing general-purpose single-view spatial understanding benchmarks does not reliably translate to success in the robotic spatial tasks assessed by our benchmark. We release MV-RoboBench as an open resource to foster progress in spatially grounded VLMs and VLAs, providing a foundation for advancing embodied multi-view intelligence in robotics.

With the growing adoption of large language model (LLM) agents in persistent, real-world roles, they naturally encounter continuous streams of tasks and interactions. A key limitation, however, is their failure to learn from this accumulated experience, forcing them to discard valuable insights and repeat past errors. Unlike prior works that primarily store raw experience or successful routines, we propose ReasoningBank, a novel memory framework that allows an agent to self-curate generalizable reasoning strategies from both its successful and failed experiences for future leverage. This mechanism enables agents to generalize across tasks and become more capable over time. To accelerate and diversify this test-time learning process, we further propose memory-aware test-time scaling (MaTTS), which leverages a powerful synergy between memory and test-time scaling. On one hand, relevant memory from ReasoningBank guides the scaling process toward more effective exploration and improved reliability. On the other, scaling, in both parallel and sequential settings, generates abundant, diverse experiences that provide rich contrastive signals for synthesizing higher-quality memory. Experiments on web browsing and software engineering tasks show that ReasoningBank consistently outperforms existing memory mechanisms in both effectiveness and efficiency, with MaTTS further amplifying the gains. These findings position memory-driven experience as a new dimension of test-time scaling, where emergent behaviors naturally arise and agents acquire self-evolving capabilities.

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings—where stale data from past policies are used for training—improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios—including sample replay and partial rollout—BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.

Recent advancements in long chain-of-thought (CoT) reasoning, particularly through the Group Relative Policy Optimization algorithm used by DeepSeek-R1, have led to significant interest in the potential of Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Models (LLMs). While RLVR promises to improve reasoning by allowing models to learn from free exploration, there remains debate over whether it truly enhances reasoning abilities or simply boosts sampling efficiency. This paper systematically investigates the impact of RLVR on LLM reasoning. We revisit Pass@K experiments and demonstrate that RLVR can extend the reasoning boundary for both mathematical and coding tasks. This is supported by our introduction of a novel evaluation metric, CoT-Pass@K, which captures reasoning success by accounting for both the final answer and intermediate reasoning steps. Furthermore, we present a theoretical framework explaining RLVR’s incentive mechanism, demonstrating how it can encourage correct reasoning even when rewards are based solely on answer correctness. Our analysis of RLVR’s training dynamics reveals that it incentivizes correct reasoning early in the process, with substantial improvements in reasoning quality confirmed through extensive evaluations. These findings provide strong evidence of RLVR’s potential to enhance LLM reasoning, offering valuable insights into its mechanisms and performance improvements.

Test-time domain generalization (TTDG) methods enhance the performance of neural networks on target domains by transferring the feature distribution of target samples to approximate that of the source domain, while avoiding the computational cost associated with fine-tuning on the target domain. However, existing TTDG methods primarily rely on style transfer strategies operating at a coarse granularity, which prove ineffective for pixel-level prediction tasks such as image super-resolution (SR). To address this limitation, we propose a multi-codebook based test-time domain generalization framework (MC-TTDG). Our method leverages both domain-specific and domain-invariant codebooks to achieve fine-grained representation learning on source domains, and performs pixel-level nearest-neighbor feature matching and transfer to accurately adjust target domain features. Furthermore, we introduce a voting-based strategy for optimal domain-specific codebook selection, which improves the precision of feature transfer through multi-party consensus. Extensive experiments across diverse data distributions, and network architectures demonstrate that the proposed method effectively transfers feature distributions for SR networks. Our code is available at https://github.com/ZaizuoTang/MC-TTDG.

Recent research has generated hope that inference scaling, such as resampling solutions until they pass verifiers like unit tests, could allow weaker models to match stronger ones. Beyond inference, this approach also enables training reasoning models, where data is curated using rejection sampling against a verifier. However, we show that this approach is fundamentally limited when verifiers are imperfect and have a non-zero probability of producing false positives. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling, regardless of compute budget. Our analysis shows that there is a strong correlation between the model’s single-sample accuracy and its false positive rate on HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model. Empirical results show that optimal sampling attempts are often fewer than 10, as the negative utility of false positives outweighs benefits, bending inference scaling curves downward. Finally, false positives may have other undesirable qualities, like poor adherence to coding style conventions.

Multimodal Large Language Models (MLLMs) have achieved notable gains in various tasks by incorporating Chain-of-Thought (CoT) reasoning in language spaces. Recent work extends this direction by leveraging external tools for visual editing, thereby enhancing the visual signal along the reasoning trajectories. Nevertheless, these approaches remain fundamentally constrained: reasoning is still confined to the language space, with visual information treated as static preconditions. We introduce Latent Visual Reasoning (LVR), a new paradigm that enables autoregressive reasoning directly in the visual embedding space. A visual encoder first projects images into visual tokens within a joint semantic space shared with the language model. The language model is then trained to generate latent states that reconstruct key visual tokens critical for answering the query, constituting the process of latent visual reasoning. By interleaving LVR with standard text generation, our model achieves substantial gains on perception-intensive visual question answering tasks. In addition, we adapt the GRPO algorithm to conduct reinforcement learning on latent reasoning, further balancing LVR and textual generation. We show that LVR substantially improves fine-grained visual understanding and perception, achieving 71.67\% on MMVP compared to 66.67\% with Qwen2.5-VL. Code base and model weights will be released later.

Automated theorem proving (ATP) --- the task of generating a proof that passes automated proof verification given a math question in formal language --- is a critical challenge at the intersection of mathematics and Artificial Intelligence (AI). We introduce Goedel-Prover-V2, a family of two language models that establish a new state-of-the-art (SOTA) in open-source ATP, using the Lean proof assistant. In addition to standard expert iteration and reinforcement learning, our approach incorporates three key innovations: (1) During training when improvement plateaus on human questions, the prover does scaffolded data synthesis to generate synthetic questions of increasing difficulty for its own training; (2) The prover is trained to self-correct using Lean compiler feedback; (3) Improved test-time exploration through checkpoint averaging to balance accuracy and diversity. Our small model, Goedel-Prover-V2-8B, reaches 84.6\% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B despite being $80\times$ smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1\% on MiniF2F at pass@32 in standard mode and 90.4\% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing first place among open-source models and surpassing DeepSeek-Prover-V2-671B's record of 47 problems by pass@1024 with about $20\times$ smaller model size and significantly lower compute budget. Our models, code, and data are released at \url{https://github.com/Goedel-LM/Goedel-Prover-V2}.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven to be a highly effective strategy for empowering Large Language Models (LLMs) with long chain-of-thought reasoning abilities. However, its design and optimizations remain tailored to purely textual domains, resulting in suboptimal performance when applied to multimodal reasoning tasks. In particular, we observe that a major source of error (67%) in current multimodal reasoning lies in the perception of visual inputs. To address this bottleneck, we propose PAPO, a novel policy gradient algorithm that encourages the model to generate visually grounded reasoning without external supervision. Specifically, we introduce the Implicit Perception Loss in the form of a KL divergence term, which maximizes the difference between two probability distributions over the same rollout sequence, conditioned on either the original or corrupted visual input. Notably, PAPO does not rely on any additional data annotation, reward models, or stronger teacher models, and can therefore be seamlessly integrated into mainstream RLVR algorithms such as GRPO and DAPO. To further enhance the training stability of PAPO, we introduce the Double Entropy Loss, which effectively regularizes the new KL objective without compromising performance. Despite its simplicity, PAPO yields significant overall improvements of 4.4%-17.5% on diverse multimodal benchmarks. The improvements are more pronounced, approaching 8.0%-19.1%, on tasks with high vision dependency. We also observe a substantial reduction of 30.5% in perception errors, indicating improved perceptual capabilities with PAPO. Overall, PAPO offers a new perspective on advancing multimodal RLVR via the optimization objective, moving beyond rollout or reward design and pointing toward deeper integration of perception and reasoning.