ICLR 2026 Papers

Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention. Although widely adopted, transformers require scaling memory and compute linearly during inference. A recent stream of work linearized the softmax operation, resulting in powerful recurrent neural network (RNN) models with constant memory and compute costs such as DeltaNet, Mamba or xLSTM. These models can be unified by noting that their recurrent layer dynamics can all be derived from an in-context regression objective, approximately optimized through an online learning rule. Here, we join this line of work and introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer (von Oswald et al., 2024), and study it in language modeling at the billion-parameter scale. This layer again stems from an in-context loss, but which is now minimized to optimality at every time point using a fast conjugate gradient solver. Through an extensive suite of experiments, we show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs, especially on tasks requiring long context understanding. This performance gain comes at the cost of additional flops spent during inference time. Our results are therefore intriguingly related to recent trends of increasing test-time compute to improve performance -- here by spending compute to solve sequential optimization problems within the neural network itself.

Large Vision-Language Models excel at multimodal understanding but struggle to deeply integrate visual information into their predominantly text-based reasoning processes, a key challenge in mirroring human cognition. To address this, we introduce DeepEyes, a model that learns to ``think with images'', trained end-to-end with reinforcement learning and without pre-collected reasoning data for supervised fine-tuning (SFT) as a cold-start. Notably, this ability emerges natively, leveraging the model's own grounding capability as an intrinsic function rather than relying on external specialized models or APIs. We enable this capability through active perception, where the model learns to strategically ground its reasoning in visual information, guided by a tailored data selection and reward strategy. DeepEyes achieves significant performance gains on general perception and reasoning benchmarks and also demonstrates improvement in grounding, hallucination, and mathematical reasoning tasks. Interestingly, we observe the distinct evolution of active perception from initial exploration to efficient and accurate exploitation, and diverse thinking patterns that closely mirror human visual reasoning processes. Code is available at \url{https://anonymous.4open.science/r/DeepEyes-97FE/}.

Large language models learn from their vast pre-training corpora, gaining the ability to solve an ever increasing variety of tasks; yet although researchers work to improve these datasets, there is little effort to understand how efficient the pre-training apparatus is at extracting ideas and knowledge from the data. In this work, we use retrieval augmented generation along with test-time compute as a way to quantify how much dataset value was left behind by the process of pre-training, and how this changes across scale. We demonstrate that pre-training then retrieving from standard and largely open-sourced datasets results in significant accuracy gains in MMLU, Math-500, and SimpleQA, which persist through decontamination. For MMLU we observe that retrieval acts as a ~5x compute multiplier versus pre-training alone. We show that these results can be further improved by leveraging additional compute at test time to parse the retrieved context, demonstrating a 10 percentage point improvement on MMLU for the public LLaMA 3.1 8B model. Overall, our results suggest that today's pre-training methods do not make full use of the information in existing pre-training datasets, leaving significant room for progress.

A central paradox in fine-tuning Large Language Models (LLMs) with Reinforcement Learning with Verifiable Reward (RLVR) is the frequent degradation of multi-attempt performance (Pass@k) despite improvements in single-attempt accuracy (Pass@1). This is often accompanied by catastrophic forgetting, where models lose previously acquired skills. Despite numerous proposed methods, the community's focus on the standard reverse KL-divergence has led to a surprising oversight: the potential of alternative f-divergences as a proactive solution has been largely unexamined. We argue that standard RLVR objectives—both those using the mode-seeking reverse KL-divergence and those forgoing a divergence term entirely—lack a crucial mechanism for knowledge retention. The reverse-KL actively accelerates this decay by narrowing the policy, while its absence provides no safeguard against the model drifting from its diverse knowledge base. We propose a fundamental shift in perspective: using the divergence term itself as the solution. Our framework, Diversity-Preserving Hybrid RL (DPH-RL), leverages mass-covering f-divergences (like forward-KL and JS-divergence) to function as a 'rehearsal mechanism'. By continuously referencing the initial policy, this approach forces the model to maintain broad solution coverage. Math and SQL generation experiments show that DPH-RL both improves in-domain Pass@1 and Pass@k scores and effectively prevents catastrophic forgetting on out-of-domain tasks. Additionally, DPH-RL is more training-efficient because it computes f-divergence using generator functions, requiring only sampling from the initial policy and no online reference model. Our work highlights a crucial, overlooked axis for improving RLVR, demonstrating that the proper selection of a divergence measure is a powerful tool for building more general and diverse reasoning models.

Long-form legal reasoning remains a key challenge for large language models (LLMs) in spite of recent advances in test-time scaling. To address this, we introduce ***LEXam***, a novel benchmark derived from 340 law exams spanning 116 law school courses across a range of subjects and degree levels. The dataset comprises 4,886 law exam questions in English and German, including 2,841 long-form, open-ended questions and 2,045 multiple-choice questions. Besides reference answers, the open questions are also accompanied by explicit guidance outlining the expected legal reasoning approach such as issue spotting, rule recall, or rule application. Our evaluation on both open-ended and multiple-choice questions present significant challenges for current LLMs; in particular, they notably struggle with open questions that require structured, multi-step legal reasoning. Moreover, our results underscore the effectiveness of the dataset in differentiating between models with varying capabilities. Deploying an ensemble LLM-as-a-Judge paradigm with rigorous human expert validation, we demonstrate how model-generated reasoning steps can be evaluated consistently and accurately, closely aligning with human expert assessments. Our evaluation setup provides a scalable method to assess legal reasoning quality beyond simple accuracy metrics. Anonymous repository: [this URL](https://anonymous.4open.science/r/LEXam-anonymous-12EB).

The maturation of Large Audio Language Models (LALMs) has raised growing expectations for them to comprehend complex audio much like humans. Current efforts primarily replicate text-based reasoning by contextualizing audio content through a one-time encoding, which introduces a critical information bottleneck. Drawing inspiration from human cognition, we propose audio-interleaved reasoning to break through this bottleneck. It treats audio as an active reasoning component, enabling sustained audio engagement and perception-grounded analysis. To instantiate it, we introduce a two-stage training framework, first teaching LALMs to localize informative audio segments through supervised fine-tuning, and then incentivizing proficient revisiting via reinforcement learning. In parallel, a structured data generation pipeline is developed to produce high-quality training data. Consequently, we present Echo, a LALM capable of dynamically revisiting audio segments in demand during reasoning. On audio comprehension benchmarks, Echo achieves overall superiority in both challenging expert-level and general-purpose tasks. Comprehensive analysis further confirms the efficiency and generalizability of audio-interleaved reasoning, establishing it as a promising direction for advancing audio comprehension. Project page: https://github.com/wdqqdw/Echo.

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient mechanism to address the above limitations via decomposing each iteration into three stages: a short fast trajectory of inner steps on the same batch, a reposition step to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces number of rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points on math reasoning benchmarks. It also achieves up to 4.93$\times$ fewer rollouts and a 4.19$\times$ reduction in wall-clock time to match GRPO’s best accuracy.

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse yet correct reasoning modes are typically deep in the sampling tree. Consequently, common strategies to encourage diversity, such as temperature scaling, encounter a worsened trade-off between diversity and accuracy. Motivated by this challenge, we treat parallel reasoning as a set-of-next-token-prediction problem and incorporate a set-based global loss into Supervised Fine-Tuning (SFT) using bipartite matching between global forking tokens and unique reasoning traces. We observe that, whereas naive fine-tuning with multiple reasoning traces collapses these unique reasoning modes, our proposed method, Set Supervised Fine-Tuning (SSFT), preserves these modes and produces emergent global forking tokens. Experiments on multiple reasoning benchmarks show our SSFT method consistently outperforms SFT under both pass@1 and cons@k metrics.

Process reward models (PRMs) are a cornerstone of test-time scaling (TTS), designed to verify and select the best responses from large language models (LLMs). However, this promise is challenged by recent benchmarks where simple majority voting, which ignores PRM signals, occasionally outperforms standard PRM-based selection. This raises a critical question: How can we effectively utilize verification signals from PRMs for TTS? To address this, we start by developing a theoretical framework for optimally combining signals from both the LLM and the PRM. Our framework reveals that the optimal strategy is a weighted aggregation of responses, a strategy whose effectiveness hinges on estimating weights that capture the complex interplay between the models. Based on our theoretical results, we empirically show that these optimal weighting functions differ significantly across LLM-PRM pairs and, notably, often assign substantial negative weights. Motivated by these insights, we propose efficient pre-computation methods to calibrate these weighting functions. Extensive experiments across 5 LLMs and 7 PRMs demonstrate that our calibration method significantly boosts the TTS efficiency, surpassing the performance of vanilla weighted majority voting while using only $\sim 21.3\\%$ of the computation. Ultimately, our work demonstrates that investing in a more intelligent aggregation strategy can be a more convincing path to performance gains than simply scaling test-time computation.

Test-time entropy minimization helps adapt a model to novel environments and incentivize its reasoning capability, unleashing the model's potential during inference by allowing it to evolve and improve in real-time using its own predictions. However, pure test-time entropy minimization can favor non-generalizable shortcuts, such as inflating the logit norm and driving all predictions to a dominant class to reduce entropy, risking collapsed solutions (e.g., constant one-hot outputs) that trivially minimize the objective without meaningful learning. In this paper, we introduce ZeroSiam, an efficient asymmetric Siamese architecture tailored for test-time entropy minimization. ZeroSiam prevents collapse through asymmetry learning, which is efficiently achieved by a learnable predictor and a stop-gradient operator before the classifier. Beyond the collapse prevention effect, we provide empirical and theoretical evidence that ZeroSiam also absorbs and regularizes biases at testing, enhancing TTA effectiveness even when no collapse occurs. Despite its simplicity, extensive results show that ZeroSiam can avoid collapse and perform more stably over prior methods using negligible overhead, demonstrating efficacy on both vision and language tasks across challenging test scenarios and diverse models, e.g., tiny based models that are particularly collapse-prone.

Preference‑based reward learning is widely used for shaping agent behavior to match a user's preference, yet its sparse binary feedback makes it especially vulnerable to causal confusion. The learned reward often latches onto spurious features that merely co‑occur with preferred trajectories during training, collapsing when those correlations disappear or reverse at test time. We introduce ReCouPLe, a lightweight framework that uses natural language rationales to provide the missing causal signal. Each rationale is treated as a guiding projection axis in embedding space, training the model to score trajectories based on features aligned with that axis while de-emphasizing context that is unrelated to the stated reason. Because identical rationales can arise across multiple tasks (e.g., "_it avoids collisions with a fragile object_"), ReCouPLe naturally reuses the same causal direction whenever tasks share semantics, and transfers preference knowledge to novel tasks without extra data or language‑model fine‑tuning. Our learned reward model can ground preferences on the articulated reason, aligning better with user intent and generalizing beyond spurious features.

LLM unlearning is essential for mitigating safety, copyright, and privacy concerns in pre-trained Large Language Models (LLMs). Compared to preference alignment, it offers a more explicit way by removing undesirable knowledge characterized by specific unlearning datasets. In previous works, Gradient Ascent (GA) and its variants have shown promise for implementing unlearning, yet their untargeted nature results in unintended degradation of general capabilities, incomplete removal of knowledge, and the generation of incoherent responses, among many others. We argue that these issues stem from the absence of explicit guidance on what and how models should unlearn. To fill this gap, we introduce a novel unlearning target, *reasoning-based unlearning target*, which satisfies both the specified unlearning scope and the specified post-unlearning response. Building on this, we propose *Targeted Reasoning Unlearning* (TRU), which leverages reasoning-based unlearning target as guidance. We employ the target using a cross-entropy supervised loss combined with a GA-based loss, enabling the model to learn reasoning ability for precise knowledge removal while preserving unrelated abilities. We evaluate TRU against strong baselines across multiple benchmarks and LLM backbones, and find that it achieves more reliable unlearning while preserving general capabilities. Moreover, TRU exhibits superior robustness under diverse attack scenarios, stemming from the reasoning ability learned through reasoning-based targets. Overall, our study establishes reasoning-augmented unlearning as a practical paradigm for reliable and explainable LLM unlearning.

The success of LLMs has sparked interest in various agentic applications. A key hypothesis is that LLMs, leveraging common sense and Chain-of-Thought (CoT) reasoning, can effectively explore and efficiently solve complex domains. However, LLM agents have been found to suffer from sub-optimal exploration and the knowing-doing gap, the inability to effectively act on knowledge present in the model. In this work, we systematically study why LLMs perform sub-optimally in decision-making scenarios. In particular, we closely examine three prevalent failure modes: greediness, frequency bias, and the knowing-doing gap. We propose mitigation of these shortcomings by fine-tuning via Reinforcement Learning (RL) on self-generated CoT rationales. Our experiments across multi-armed bandits, contextual bandits, and Tic-tac-toe demonstrate that RL fine-tuning enhances the decision-making abilities of LLMs by increasing exploration and narrowing the knowing-doing gap. Finally, we study both classic exploration mechanisms, such as $\epsilon$-greedy, and LLM-specific approaches, such as self-correction and self-consistency, to enable more effective fine-tuning of LLMs for decision-making.

Learning in the combinatorially large output space of sequence generation problems is challenging as providing expert demonstrations scales poorly with sequence length, and RL struggles with sparse rewards. Between dense demonstrations in supervised training and no demonstrations in reinforcement learning lies an underexplored regime: partial supervision. We ask whether some classes of sequence learning problems become efficiently learnable by exploiting this gap. We address this by introducing adaptive backtracking (AdaBack), a per-sample curriculum learning algorithm that reveals a partial prefix of the target output. The supervision length is adjusted dynamically for each sample based on the model’s past reward signal, allowing it to incrementally learn to complete reasoning chains by conditioning on correct partial solutions. We investigate this intermediate regime between SFT and RL and argue that per-sample curriculum learning is more than a trade-off between efficiency and generality—it can succeed in tasks with long sequences of latent dependencies where SFT and RL both fail to generalize. Using a synthetic task with latent parity constraints, we show that AdaBack reliably solves problems that are otherwise intractable. On two mathematical reasoning benchmarks, MATH and GSM8k, we find that AdaBack enables models to solve problems that RL alone cannot, acquiring new reasoning capabilities through incremental exposure to partial solutions.

Emotional information in speech plays a unique role in multimodal perception. However, current Speech Large Language Models (SpeechLLMs), similar to conventional speech emotion recognition (SER) systems, still treat emotion understanding as a simple classification problem. This provides limited interpretability of predictions, while leaving the LLMs’ expressive and reasoning capabilities underutilized. In this work, we take the first step to reformulate SER as a deep reasoning problem through reinforcement learning (RL). We propose EmotionThinker, which is designed to generate accurate emotion predictions with interpretable explanations grounded in fine-grained acoustic cues. To achieve this, we first construct EmotionCoT-35K, an emotional reasoning dataset with Chain-of-Thought annotations and detailed captions. Second, we observe that current SpeechLLMs exhibit weak prosody perception, whereas prosodic cues constitute fundamental signals for interpreting emotions. To address this, we develop the prosody-enhanced foundation model EmotionThinker-Base, and demonstrate that prosody enhancement improves emotion understanding. Third, we introduce Group-Relative-Policy-Optimization with Progressive-Trust-aware-Reasoning-Reward (GRPO-PTR}) for RL. Different from standard GRPO, which relies only on rule-based outcome rewards, GRPO-PTR progressively introduces reasoning reward, dynamically adjusts it with a trustworthiness weight reflecting the alignment between reasoning and outcome, and evaluates the overall reasoning quality with a reward model based on multi-dimensional criteria. EmotionThinker outperforms previous state-of-the-art evaluation models both in emotion accuracy and explanation quality, advancing SER toward interpretable multimodal reasoning.

While Large Language Models (LLMs) show immense promise as planners for embodied AI, their stochastic nature and lack of formal reasoning capabilities prevent the strict safety guarantees required for physical deployment. Current approaches fall short: they either rely on other unreliable LLMs for safety checks or simply reject unsafe plans without offering a path to success. This work bridges this critical gap by introducing the Verifiable Iterative Refinement Framework (VIRF), a neuro-symbolic architecture that shifts the paradigm from a passive safety gatekeeper to an active safety collaborator. Where prior verifiers simply reject failures, our framework provides causal, pedagogical feedback that teaches the LLM why its plan was unsafe, enabling intelligent repairs rather than mere avoidance.Our core contribution is a novel tutor-apprentice dialogue, where a deterministic Logic Tutor, grounded in a formal safety ontology, provides causal and explanatory feedback to an LLM Apprentice planner. This pedagogical interaction allows the apprentice to perform intelligent, creative plan repairs, resolving safety conflicts rather than merely avoiding them. To ground this dialogue in verifiable truth, we introduce a scalable knowledge acquisition pipeline that synthesizes a comprehensive safety knowledge base from real-world documents, a process that simultaneously reveals and corrects significant blind spots in existing benchmarks. On a new suite of challenging home safety tasks, VIRF achieves a perfect 0\% Hazardous Action Rate (HAR), completely eliminating unsafe actions while attaining a 77.3\% Goal-Condition Rate (GCR)—the highest among all baselines. It does so with remarkable efficiency, requiring only 1.1 correction iterations on average. By acting as a verifiable safety scaffold, VIRF demonstrates a principled and robust pathway toward building embodied agents that are not just capable, but fundamentally trustworthy.

Multimodal models have achieved remarkable progress, yet recent studies suggest they struggle with compositional reasoning, often performing at or below random chance on established benchmarks. We revisit this problem and show that widely used evaluation metrics systematically underestimate model capabilities. To address this, we introduce a group matching score that better leverages group structure and uncovers substantial hidden competence in both contrastive vision–language models (VLMs) and multimodal large language models (MLLMs). Moreover, simply overfitting to the induced group matchings at test time transfers this hidden competence into higher scores under the original evaluation metric, closing much of the reported gap. With this adjustment, GPT-4.1 becomes the first system to surpass estimated human performance on Winoground. Building on this insight, we propose Test-Time Matching (TTM), an iterative self-training algorithm that bootstraps model performance without any external supervision. TTM delivers further non-trivial improvements: for example, SigLIP-B16 with TTM surpasses GPT-4.1 on MMVP-VLM, establishing a new state of the art. Importantly, TTM is broadly effective even on benchmarks without metric-induced effects or group structures, achieving relative gains exceeding 85.7\% on challenging datasets such as Whatsup. Across 16 datasets and variants, our experiments consistently demonstrate that TTM unlocks hidden compositional reasoning ability and advances the frontier of multimodal evaluation.

We present **Lean4PHYS**, a comprehensive reasoning framework for college-level physics problems in Lean4. **Lean4PHYS** includes *LeanPhysBench*, a college-level benchmark for Lean4 formal physics reasoning, which contains 200 hand-crafted and peer-reviewed statements formalized from university textbooks and physics competition problems. To establish a solid foundation for formal reasoning in physics, we also launch *PhysLib*, a repository that contains fundamental unit systems and theorems essential for formal physics proving, which aims to be community-driven and long-term maintained. Based on the *LeanPhysBench* and *PhysLib* we composed in **Lean4PHYS**, we perform exhaustive experiments of baseline results using major expert Math Lean4 provers and state-of-the-art closed-source models, and provide an analysis of their performance. In the experiment, we identify that most expert provers do not outperform general models as they did in the math domain. This indicates a potential overfitting of the math domain rather than learning formal reasoning for formal provers. We also conduct a comprehensive experiment showing that with *PhysLib* in the context, LLMs' performance on *LeanPhysBench* increases by 11.90\% on average, proving the effectiveness of our repository in assisting LLMs to solve the Lean4 physics problem. To the best of our knowledge, we are the first study to provide a physics benchmark in Lean4.

Parallel thinking has emerged as a novel approach for enhancing the reasoning capabilities of large language models (LLMs) by exploring multiple reasoning paths concurrently. However, activating such capabilities through training remains challenging. Existing methods mainly rely on supervised fine-tuning (SFT) over synthetic data, which encourages teacher-forced learning rather than exploration and generalization. To address this issue, we propose **Parallel-R1**, the first reinforcement learning (RL) framework that instills parallel thinking for complex real-world reasoning tasks. Our framework employs a progressive curriculum that addresses the cold-start problem in training parallel thinking with RL. We first use SFT on prompt-generated trajectories from easier tasks to instill the parallel thinking behavior, then transition to RL to explore and generalize this skill on harder problems. Experiments on various math benchmarks, including MATH, AMC23, and AIME, show that Parallel-R1 successfully elicits parallel thinking, leading to 8.4% accuracy improvements over the sequential thinking model trained directly on difficult tasks with RL. Further analysis reveals a distinct shift in the model's thinking patterns: in the early stage, it utilizes parallel thinking as an exploration strategy, while in the later stage, it employs this ability for multi-perspective verification. Most significantly, we validate parallel thinking as a **mid-training exploration scaffold**, where this intermediate phase unlocks a higher performance ceiling after RL, yielding a **42.9%** improvement over the sequential RL baseline.