ICLR 2026 Papers

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement algorithmic procedures that can be used to deduce answers to hard problems. Doing so requires reusing primitives, intermediate results, or procedures across multiple problems. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, the depth-first and brute-force nature of reasoning traces learned by these models suggests that this is far from a fulfilled promise. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing several useful abstractions given a problem, followed by RL training that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and an abstraction-conditioned solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that spending more test-time compute into generating abstractions is more beneficial for performance than generating more solutions at large inference-time budgets, illustrating the role of abstractions in guiding global exploration.

Transformer LLMs have been shown to exhibit strong reasoning ability that scales with inference-time compute, most prominently through token-space “thinking” (i.e., chains of thought). A growing line of work pushes this extra computation into the model’s latent space (adjacent to standard decoding) which we term Auxiliary Latent-Space Computation (ALSC). Existing ALSC methods largely fall into three buckets: (i) token-mediated latent or special-token rollouts, (ii) residual/activation steering, and (iii) memory compression via cache pruning, merging, or summarization. An underexplored alternative is memory consolidation and reconsolidation, two processes in the brain that are responsible for stabilising newly formed memory traces, and, upon recall, transiently rendering established traces plastic such they can integrate new contextual information before restabilising. In a Transformer LLM, this can be seen as analogous to performing in-place global rewrites of incoming KV segments, and rewrites of past segments conditioned on newly observed tokens. In this work, we give a theoretical justification as to why memory (re)consolidation via KV cache rewrites is beneficial for improved reasoning. We do this through the lens of Information Bottleneck (IB) theory, which posits that model generalisation emerges from an optimal balance between input information compression and retention of predictive information in latent representations. We prove using IB theory that Vanilla decoder-only Transformers are inherently constrained in their ability to form task-optimal sequence representations. We then introduce the Bottlenecked Transformer, which augments a decoder-only backbone LLM with a lightweight Cache Processor, an auxiliary Transformer that performs periodic, non-causal, in-place KV rewrites at newline-delimited reasoning step boundaries. The processor consolidates recently written KV entries and reconsolidates a small, top-$k$ attention-selected set of prior entries, conditioned on recent context. We evaluate our Bottlenecked Transformer architecture on seven mathematical reasoning benchmarks, with four backbone LLMs. Our model sees consistent performance gains over vanilla Transformers and pause-token augmented Transformer baselines, with gains of up to +6.6pp for selected tasks and backbones.

Chain-of-Thought (CoT) reasoning has advanced the capabilities and transparency of language models (LMs); however, reasoning chains can contain inaccurate statements that reduce performance and trustworthiness. To address this, we propose to augment each reasoning step in a CoT with a latent veracity (or correctness) variable. To efficiently explore this expanded space, we introduce Veracity Search (VS), a discrete search algorithm over veracity assignments. It performs otherwise intractable inference in the posterior distribution over latent veracity values by leveraging the LM's joint likelihood over veracity and the final answer as a proxy reward. This efficient inference-time verification method facilitates supervised fine-tuning of an Amortized Veracity Inference (AVI) machine by providing pseudo-labels for veracity. AVI generalizes VS, enabling accurate zero-shot veracity inference in novel contexts. Empirical results demonstrate that VS reliably identifies errors in logical (ProntoQA), mathematical (GSM8K), and commonsense (CommonsenseQA) reasoning benchmarks, with AVI achieving comparable zero-shot accuracy. Finally, we demonstrate the utility of latent veracity inference for providing feedback during self-correction and self-improvement.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities in complex problem-solving tasks, sparking growing interest in their application to preference reasoning in recommendation systems. Existing methods typically rely on fine-tuning with explicit chain-of-thought (CoT) data. However, these methods face significant practical limitations due to (1) the difficulty of obtaining high-quality CoT data in recommendation and (2) the high inference latency caused by generating CoT reasoning. In this work, we explore an alternative approach that shifts from explicit CoT reasoning to compact, information-dense latent reasoning. This approach eliminates the need for explicit CoT generation and improves inference efficiency, as a small set of latent tokens can effectively capture the entire reasoning process. Building on this idea, we propose *Reinforced Latent Reasoning for Recommendation* (LatentR$^3$), a novel end-to-end training framework that leverages reinforcement learning (RL) to optimize latent reasoning without relying on any CoT data.LatentR$^3$ adopts a two-stage training strategy: first, supervised fine-tuning to initialize the latent reasoning module, followed by pure RL training to encourage exploration through a rule-based reward design. Our RL implementation is based on a modified GRPO algorithm, which reduces computational overhead during training and introduces continuous reward signals for more efficient learning. Extensive experiments demonstrate that LatentR$^3$ enables effective latent reasoning without any direct supervision of the reasoning process, significantly improving performance when integrated with different LLM-based recommendation methods. Our codes are available at https://anonymous.4open.science/r/R3-A278/.

Large Language Models (LLMs) excel at multi-step reasoning problems with explicit chain-of-thought (CoT), but verbose traces incur significant computational costs and memory overhead, and often carry redundant, stylistic artifacts. Latent reasoning has emerged as an efficient alternative that internalizes the thought process, but it suffers from a critical lack of supervision, limiting its effectiveness on complex, natural-language reasoning traces. In this work we propose KaVa, the first framework that bridges this gap by distilling knowledge directly from a compressed KV-cache of the teacher into a latent-reasoning student via self-distillation, leveraging the representational flexibility of continuous latent tokens to align stepwise KV trajectories. We show that the abstract, unstructured knowledge within compressed KV-cache, which lacks direct token correspondence, can serve as a rich supervisory signal for a latent reasoning student. Empirically, the approach consistently outperforms strong latent baselines, exhibits markedly smaller degradation from equation-only to natural-language traces, and scales to larger backbones while preserving efficiency. These results establish compressed KV-cache distillation as a scalable supervision signal for latent reasoning, combining the accuracy of CoT-trained teachers with the efficiency and deployability of latent inference.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BAM (Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the E3 metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to 70% accuracy gains, 39% token reduction, and 193.8% improvement in E3. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B), demonstrating Plan-and-Budget’s ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

Web agents promise to automate complex browser tasks, but current methods remain brittle -- relying on step-by-step UI interactions and heavy LLM reasoning that break under dynamic layouts and long horizons. Humans, by contrast, exploit website-provided functionality through high-level operations like search, filter, and sort. We introduce WALT (Web Agents that Learn Tools), a framework that reverse-engineers latent website functionality into deterministic, callable tools. Rather than hypothesizing ad-hoc skills, WALT exposes robust implementations of automations already designed into websites, spanning discovery (search, filter, sort), communication (post, comment, upvote), and content management (create, edit, delete). Tools abstract away low-level execution: instead of reasoning about how to click and type, agents simply call search(query) or create(listing). This shifts the computational burden from fragile step-by-step reasoning to reliable tool invocation. On VisualWebArena and WebArena, WALT achieves significantly higher success rates with fewer steps and less LLM-dependent reasoning, establishing a robust and generalizable paradigm for browser automation.

The development of autonomous agents for complex, long-horizon tasks is a central goal in AI. However, dominant training paradigms face a critical limitation: reinforcement learning (RL) methods that optimize solely for final task success often reinforce flawed or inefficient reasoning paths, a problem we term inefficient exploration. This leads to agents that are brittle and fail to generalize, as they learn to find solutions without learning how to reason coherently. To address this, we introduce RLVMR, a novel frame-work that integrates dense, process-level supervision into end-to-end RL by rewarding verifiable, meta-reasoning behaviors. RLVMR equips an agent to explicitly tag its cognitive steps—such as planning, exploration, and reflection—and provides program-matic, rule-based rewards for actions that contribute to effective problem-solving. These process-centric rewards are combined with the final outcome signal and optimized using a critic-free policy gradient method. On the challenging ALFWorld and ScienceWorld benchmarks, RLVMR achieves new state-of-the-art results, with our 7B model reaching an 83.6% success rate on the most difficult unseen task split. Our analysis confirms these gains stem from improved reasoning quality, including significant reductions in redundant actions and enhanced error recovery, leading to more robust, efficient, and interpretable agents.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they often suffer from overthinking, expending redundant computational steps on simple problems, or underthinking, failing to explore sufficient reasoning paths despite inherent capabilities. These issues lead to inefficiencies and potential inaccuracies, limiting practical deployment in resource-constrained settings. Existing methods to mitigate overthinking, such as suppressing reflective keywords or adjusting reasoning length, may inadvertently induce underthinking, compromising accuracy. Therefore, we propose \textsc{ReBalance}, a training-free framework that achieves efficient reasoning with balanced thinking. \textsc{ReBalance} leverages confidence as a continuous indicator of reasoning dynamics, identifying overthinking through high confidence variance and underthinking via consistent overconfidence. By aggregating hidden states from a small-scale dataset into reasoning mode prototypes, we compute a steering vector to guide LRMs’ reasoning trajectories. A dynamic control function modulates this vector’s strength and direction based on real-time confidence, pruning redundancy during overthinking, and promoting exploration during underthinking. Extensive experiments conducted on four models ranging from 0.5B to 32B, and across nine benchmarks in math reasoning, general question answering, and coding tasks demonstrate that \textsc{ReBalance} effectively reduces output redundancy while improving accuracy, offering a general, training-free, and plug-and-play strategy for efficient and robust LRM deployment. Code and models will be made publicly available.

Large Language Models (LLMs) for formal theorem proving have shown significant promise, yet they often lack generalizability and are fragile to even minor transformations of problem statements. To address this limitation, we introduce a novel data augmentation pipeline designed to enhance model robustness from two perspectives: symmetry and difficulty. From the symmetry perspective, we propose two complementary methods: **EvolAST**, an Abstract Syntax Tree (AST) based approach that targets syntactic symmetry to generate semantically equivalent problem variants, and **EvolDomain**, which leverages LLMs to address semantic symmetry by translating theorems across mathematical domains. From the difficulty perspective, we propose **EvolDifficulty**, which uses carefully designed evolutionary instructions to guide LLMs in generating new theorems with a wider range of difficulty. We then use the evolved data to train **EvolProver**, a 7B-parameter non-reasoning theorem prover. EvolProver establishes a new state-of-the-art (SOTA) on FormalMATH-Lite with a 53.8\% pass@32 rate, surpassing all models of comparable size, including reasoning-based models. It also sets new SOTA records for non-reasoning models on MiniF2F-Test (69.8\% pass@32), Ineq-Comp-Seed (52.2\% pass@32), and Ineq-Comp-Transformed (34.0\% pass@32). Ablation studies further confirm our data augmentation pipeline's effectiveness across multiple benchmarks.

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3\% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

While 4-bit quantization has emerged as a memory-optimal choice for non-reasoning models and zero-shot tasks across scales, we show that this universal prescription fails for reasoning models, where KV cache rather than model size can dominate memory. Through systematic experiments on mathematical, code generation, and knowledge-intensive reasoning tasks, we find a scale-dependent trade-off: models with an effective size below 8-bit 4B parameters achieve better accuracy by allocating memory to larger weights, rather than longer generation, while larger models benefit from the opposite strategy. This scale threshold also determines when parallel scaling becomes memory-efficient and whether KV cache eviction outperforms KV quantization. Our findings show that memory optimization for LLMs cannot be scale-agnostic, while providing principled guidelines: for small reasoning models, prioritize model capacity over test-time compute, while for large ones, maximize test-time compute. Our results suggest that optimizing reasoning models for deployment requires fundamentally different strategies than those established for non-reasoning ones.

We discover a novel and surprising phenomenon of unintentional misalignment in reasoning language models (RLMs), which we call \textit{self-jailbreaking}. Specifically, after benign reasoning training on math or code domains, RLMs will use multiple strategies to circumvent their own safety guardrails. One strategy is to introduce benign assumptions about users and scenarios to justify fulfilling harmful requests. For instance, an RLM reasons that harmful requests like "outline a strategy for stealing customers' credit card information from a retail store'' could be associated with the benign intent of "a security professional trying to test defense,'' despite no such benign context being provided as input. We observe that many open-weight RLMs, including DeepSeek-R1-distilled, s1, Phi-4-mini-reasoning, and Nemotron, suffer from self-jailbreaking despite being aware of the harmfulness of the requests. We also provide a mechanistic interpretation of self-jailbreaking: RLMs are more compliant after benign reasoning training, and self-jailbreaking reduces the perceived harmfulness of malicious requests so models can comply with them. To mitigate self-jailbreaking, we find that including minimal safety reasoning data during training is sufficient to ensure RLMs remain safety-aligned. Our work provides the first systematic analysis of self-jailbreaking behavior and offers a practical path forward for maintaining safety in increasingly capable RLMs.

The dominant paradigm for training large reasoning models—combining Supervised Fine-Tuning (SFT) with Reinforcement Learning with Verifiable Rewards (RLVR)—is fundamentally constrained by its reliance on high-quality, human-annotated reasoning data and external verifiers. This dependency incurs significant data-collection costs, risks embedding human cognitive biases, and confines the reinforcement learning stage to objectively assessable domains like mathematics and coding, leaving a vast landscape of unverifiable tasks unaddressed. To overcome these limitations, we introduce Native Reasoning Training (NRT), a novel framework that cultivates complex reasoning by having the model generate its own reasoning traces using only standard question-answer pairs, thereby obviating the need for expert-written demonstrations. NRT reframes the training problem by treating the reasoning process as a latent variable. It employs a unified training objective that models reasoning as an optimization problem, intrinsically rewarding paths that increase the model's likelihood of producing the ground-truth answer. This unified perspective allows us to analyze intrinsic failure modes of prior methods, such as policy collapse, and systematically design more robust reward aggregation functions, creating a self-correcting feedback loop where the model learns to \textit{think} in ways that resolve its own uncertainty. Empirical evaluation on Llama and Mistral model families demonstrates that NRT achieves state-of-the-art performance among verifier-free methods, significantly outperforming standard SFT baselines and prior verifier-free RL methods. Our approach yields particularly strong performance gains in complex reasoning domains and exhibits high robustness to policy collapse, offering a general, scalable path toward building more powerful and broadly applicable reasoning systems.

Reasoning LLMs (RLLMs) generate step-by-step chains of thought (CoTs) before giving an answer, which improves performance on complex tasks and makes reasoning transparent. But how robust are these reasoning traces to disruptions that occur within them? To address this question, we introduce a controlled evaluation framework that perturbs a model’s own CoT at fixed timesteps. We design seven interventions (benign, neutral, and adversarial) and apply them to multiple open-weight RLLMs across MATH, SCIENCE, and LOGIC tasks. Our results show that RLLMs are generally robust, reliably recovering from diverse perturbations, with robustness improving with model size and degrading when interventions occur early. However, robustness is not style-invariant: paraphrasing suppresses doubt-like expressions and reduces performance, while other interventions trigger doubt and support recovery. Recovery also carries a cost: neutral and adversarial noise can inflate CoT length by more than 200%, whereas paraphrasing shortens traces but harms accuracy. These findings provide new evidence on how RLLMs maintain reasoning integrity, identify doubt as a central recovery mechanism, and highlight trade-offs between robustness and efficiency that future training methods should address.

We propose **FROST**, an attention-aware method for efficient reasoning. Unlike traditional approaches, FROST leverages attention weights to prune uncritical reasoning paths, yielding shorter and more reliable reasoning trajectories. Methodologically, we introduce the concept of *reasoning outliers* and design an attention-based mechanism to remove them. Theoretically, FROST preserves and enhances the model’s reasoning capacity while eliminating outliers at the sentence level. Empirically, we validate FROST on four benchmarks using two strong reasoning models (Phi-4-Reasoning and GPT-oss-20B), outperforming state-of-the-art methods such as TALE and ThinkLess. Notably, FROST achieves an average **69.68%** reduction in token usage and a **26.70%** improvement in accuracy over the base model. Furthermore, in evaluations of attention outlier metrics, FROST reduces the maximum infinity norm $\||\mathbf{x}\||_{\infty}$ by **15.97%** and the average kurtosis by **91.09%** compared to the base model.

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.

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.

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.