ICLR 2026 Papers

Recently, visualization-of-thought (VoT) has unlocked new opportunities for complex spatial reasoning in multimodal large language models (MLLMs) by complementing verbal reasoning with visual thinking. However, the autoregressive accumulation of lengthy and redundant tokens substantially increases computation and memory costs. In this paper, we present a new efficient framework for multimodal spatial reasoning, named *DARE*, designed to adaptively prune multimodal tokens across different network depths, reasoning hops, and modalities. First, *DARE* devises an intra- and inter-hop-aware differentiable retention mechanism to dynamically estimate token importance both within each reasoning step and across successive hops. Recognizing that deeper network layers encode visual cues into verbal streams, *DARE* introduces an asymmetric compression strategy that prunes tokens according to modality-specific redundancy and semantic importance. Furthermore, *DARE* incorporates a progressive KV-cache retention policy aligned with cross-modal fusion dynamics, further reducing memory overhead during autoregressive reasoning. Our method delivers substantial reductions in computation and memory footprint, averaging a 40.37\% reduction in FLOPs and 46.07\% reduction in KV caches usage, while consistently preserving or even improving reasoning performance across seven multimodal spatial reasoning benchmarks, and further generalizing to broader multimodal reasoning tasks, establishing a scalable and robust recipe for efficient multimodal reasoning.

While test-time scaling with verification has shown promise in improving the performance of large language models (LLMs), role of the verifier and its imperfections remain underexplored. The effect of verification manifests through interactions of three quantities: (i) the generator’s *coverage*, (ii) the verifier’s *region of convergence* (ROC), and (iii) the sampling algorithm’s *sub-optimality*. Though recent studies capture subsets of these factors, a unified framework quantifying the geometry of their interplay is missing. We frame verifiable test-time scaling as a transport problem. This characterizes the interaction of coverage, ROC, and sub-optimality, and uncovers that the sub-optimality–coverage curve exhibits three regimes. A *transport regime* -- where sub-optimality increases with coverage, a *policy improvement regime* -- where sub-optimality may decrease with coverage, depending on the verifier’s ROC, and a *saturation regime* -- where sub-optimality plateaus, unaffected by coverage. We further propose and analyze two classes of sampling algorithms -- *sequential* and *batched*, and examine how their computational complexities shape these trade-offs. Empirical results with \texttt{Qwen}, \texttt{Llama}, and \texttt{Gemma} models corroborate our theoretical findings.

Transformers are remarkably versatile and their design is largely consistent across a variety of applications. But are they optimal for any given task or dataset? The answer may be key for pushing AI beyond merely scaling current designs. **Method.** We present a method to optimize a transformer architecture for a given dataset, which we use as a tool to study optimal task-specific inductive biases. This method replaces the most important non-linearities (GeLUs,;softmax) with functions learned on held-out data. We then train the resulting architectures on other datasets, as a way to evaluate the compatibility between pairs of tasks. **Findings.** On algorithmic toy tasks, we identify new architectures with dramatic improvements in learning speed, in- and out-of-distribution generalization, and stability across seeds. The new designs prove very task-specific however, and indicate that these tasks require inductive biases very different from those of standard transformers. On code and language modeling datasets, we also find architectures with consistent, yet smaller improvements. These designs transfer much better across datasets and domains (English & computer code). **Implications.** Our results show that standard transformers are rarely a local optimum in the space of architectures. Simple alternatives can perform much better but sacrifice universality. This suggests that there may be room for improved architectures that better support multiple capabilities simultaneously, such as fluency and robust reasoning.

Large language models (LLMs) have achieved remarkable performance across diverse reasoning tasks, yet their deployment is hindered by prohibitive computational and memory costs. Quantization-aware training (QAT) enables ultra-low-bit compression (<4 bits per weight), but existing QAT methods often degrade reasoning capability, partly because complex knowledge structures are introduced during the post-training process in LLMs. In this paper, through a systematic investigation of how quantization affects different data domains, we find that its impact on pre-training and reasoning capabilities differs. Building on this insight, we propose a novel two-stage QAT pipeline specifically designed for reasoning LLMs. In the first stage, we quantize the model using mixed-domain calibration data to preserve essential capabilities across domains; in the second stage, we fine-tune the quantized model with a teacher-guided reward-rectification loss to restore reasoning capability. We first demonstrate that mixed-domain calibration outperforms single-domain calibration by up to 2.74% improvement on average over six tasks, including reasoning and pre-trained tasks. Following experiments on five reasoning benchmarks show that our 2-bit-quantized Qwen3-8B outperforms post-training quantization (PTQ) baselines by 50.45% on average. Moreover, compared to ultra-low-bit-specialized models such as BitNet-2B4T, our pipeline achieves about 2% higher mathematical-reasoning accuracy using only 40K training sequences.

Large language models (LLMs) often exhibit flawed reasoning ability that undermines reliability. Existing approaches to improving reasoning typically treat it as a general and monolithic skill, applying broad training that is inefficient and unable to target specific reasoning errors. We introduce Reasoning Editing, a paradigm for selectively modifying specific reasoning patterns in LLMs while preserving other reasoning pathways. This task presents a fundamental trade-off between Generality, the ability of an edit to generalize across different tasks sharing the same reasoning pattern, and Locality, the ability to preserve other reasoning capabilities. Through systematic investigation, we uncover the Circuit-Interference Law: edit interference between reasoning patterns is proportional to the overlap of their neural circuits. Guided by this principle, we propose REdit, the first framework to actively reshape neural circuits before editing, thereby modulating interference between reasoning patterns and mitigating the trade-off. REdit integrates three components: (i) Contrastive Circuit Reshaping, which directly addresses the generality-locality trade-off by disentangling overlapping circuits; (ii) Meta-Contrastive Learning, which extends transferability to novel reasoning patterns; and (iii) Dual-Level Protection, which preserves preexisting abilities by constraining reshaping update directions and regularizing task-level predictions. Extensive experiments with Qwen-2.5-3B on propositional logic reasoning tasks across three difficulty levels demonstrate that REdit consistently achieves superior generality and locality compared to baselines, with additional validation in mathematics showing broader potential. Our code is available at https://anonymous.4open.science/r/REdit-DBD8.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language “reasoning chains”, their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or “hallucinate”) in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score—a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations—outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this limitation by enabling large language models (LLMs) to generate soft, abstract tokens, thus facilitating reasoning within a continuous concept space. In this paper, we investigate the $\textit{Soft Thinking}$ capabilities of various LLMs through a systematic analysis of their internal behavior using a suite of probing techniques. Contrary to the prevailing belief that Soft Thinking supports parallel exploration of diverse reasoning paths, our findings reveal that $\textbf{LLMs behave as single-threaded reasoners}$—they predominantly rely on the token with the highest probability in the soft input to predict the next step. This behavior induces a greedy feedback loop that suppresses alternative reasoning paths and undermines the benefits of transmitting richer information via Soft Tokens. To address this $\textit{Greedy Pitfall}$, we propose $\textbf{Stochastic Soft Thinking}$, which introduces stochasticity to break free from the greedy tendency. Our experiments demonstrate that incorporating $\textit{randomness}$—particularly with the $\textbf{Gumbel-Softmax trick}$—can alleviate the limitations of vanilla approaches and unleash the potential of Soft Thinking, resulting in superior performance across eight reasoning benchmarks.

There is a growing interest in Universal Multimodal Embeddings (UME), where models are required to generate task-specific representations. While recent studies show that Multimodal Large Language Models (MLLMs) perform well on such tasks, they treat MLLMs solely as encoders, overlooking their generative capacity. However, such an encoding paradigm becomes less effective as instructions become more complex and require compositional reasoning. Inspired by the proven effectiveness of chain-of-thought reasoning, we propose a general Think-Then-Embed (TTE) framework for UME, composed of a reasoner and an embedder. The reasoner MLLM first generates reasoning traces that explain complex queries, followed by an embedder that produces representations conditioned on both the original query and the intermediate reasoning. This explicit reasoning step enables more nuanced understanding of complex multimodal instructions. Our contributions are threefold. First, by leveraging a powerful MLLM reasoner, we achieve state-of-the-art performance on the MMEB-V2 benchmark, surpassing proprietary models trained on massive in-house datasets. Second, to reduce the dependency on large MLLM reasoners, we finetune a smaller MLLM reasoner using high-quality embedding-centric reasoning traces, achieving the best performance among open-source models with a 7% absolute gain over recently proposed models. Third, we investigate strategies for integrating the reasoner and embedder into a unified model for improved efficiency without sacrificing performance.

Recent frontier models employ long-chain-of-thought reasoning to explore solution spaces in context and achieve stronger performance. While many works study distillation to build smaller yet capable models, most focus on English and little is known about language-specific reasoning. To bridge this gap, we first introduce **Language-Mixed CoT**, a reasoning schema that switches between English and a target language, using English as an anchor to excel in reasoning while minimizing translation artifacts. As a Korean case study, we curate **Yi-Sang-HQ**: 5.79M native-Korean prompts from web Q&A, exams, STEM, and code; 3.7M long reasoning traces generated from Qwen3-32B; and a targeted 260k high-yield subset. We train nine models (4B–35B) across six families (Qwen2.5, Llama-3.1, Gemma-3, etc). Our best model, **KO-REAson-35B**, achieves state-of-the-art performance, with the highest overall average score ($64.0_{\pm2.5}$), ranking first on 5/9 benchmarks and second on the remainder. Smaller and mid-sized models also benefit substantially, with an average improvement of $+18.6$ points across the evaluated nine benchmarks. Ablations show **Language-Mixed CoT** is more effective than monolingual CoT, indicating that reasoning patterns can be engineered to improve non-English performance. We release our data-curation pipeline, evaluation system, datasets, and models to advance research on language-specific reasoning.

Reinforcement Learning (RL) has become a compelling way to strengthen the multi step reasoning ability of Large Language Models (LLMs). However, prevalent RL paradigms still lean on sparse outcome-based rewards and limited exploration, which often drives LLMs toward repetitive and suboptimal reasoning patterns. In this paper, we study the central question of how to design exploration for LLM reasoning and introduce MERCI (Motivating Exploration in LLM Reasoning with Count-based Intrinsic Rewards), a novel RL algorithm that augments policy optimization with a principled intrinsic reward. Building on the idea of count-based exploration, MERCI leverages a lightweight Coin Flipping Network (CFN) to estimate the pseudo count and further epistemic uncertainty over reasoning trajectories, and converts them into an intrinsic reward that values novelty while preserving the learning signal from task rewards. We integrate MERCI into some advanced RL frameworks like Group Relative Policy Optimization (GRPO). Experiments on complex reasoning benchmarks demonstrate that MERCI encourages richer and more varied chains of thought, significantly improves performance over strong baselines, and helps the policy escape local routines to discover better solutions. It indicates that our targeted intrinsic motivation can make exploration reliable for language model reasoning.

Retrieval augmentation has primarily been studied in limited settings, such as factoid question answering; more challenging, reasoning-intensive benchmarks have seen limited success from minimal RAG. In this work, we challenge this prevailing view on a set of established, reasoning-intensive benchmarks: MMLU, MMLU Pro, AGI Eval, GPQA, and MATH. We identify a key missing component in prior work: a usable, web-scale datastore aligned with the breadth of pretraining data. To this end, we introduce CompactDS: a diverse, high-quality, web-scale datastore that achieves high retrieval accuracy and subsecond latency on a single-node deployment, making it suitable for academic use. Its core design combines a compact set of high-quality, diverse data sources with in-memory approximate nearest neighbor (ANN) retrieval and on-disk exact search. Using CompactDS, a minimal RAG pipeline achieves consistent accuracy improvements across all benchmarks and model sizes (8B--70B), with relative gains of 11% on MMLU, 34% on MMLU Pro, 26% on GPQA, and 14% on MATH. No single data source suffices alone, highlighting the importance of diversity of sources (web crawls, curated math, academic papers, textbooks), and a combination of ANN and exact search is shown to be critical for balancing usability and accuracy. Finally, we show that our in-house datastore even outperforms commercial search engines like Google Search. We release CompactDS and our retrieval pipeline as a fully reproducible alternative to commercial search, supporting future research exploring retrieval-based AI systems.

Large language model (LLM) agents are increasingly tasked with complex real-world analysis (e.g., in financial forecasting, scientific discovery), yet their reasoning suffers from stochastic instability and lacks a verifiable, compositional structure. To address this, we introduce **Analytica**, a novel agent architecture built on the principle of **Soft Propositional Reasoning (SPR)**. SPR reframes complex analysis as a structured process of estimating the soft truth values of different outcome propositions, allowing us to formally model and minimize the estimation error in terms of its bias and variance. Analytica operationalizes this through a parallel, divide-and-conquer framework that systematically reduces both sources of error. To reduce bias, problems are first decomposed into a tree of subpropositions, and tool-equipped LLM *grounder agents* are employed —including a novel Jupyter Notebook agent for data-driven analysis—that help to validate and score facts. To reduce variance, Analytica recursively synthesizes these grounded leaves using robust linear models that average out stochastic noise with superior efficiency, scalability, and enable interactive "what-if" scenario analysis. Our theoretical and empirical results on economic, financial, and political forecasting tasks show that Analytica improves 15.84\% accuracy on average over diverse base models, achieving 71.06\% accuracy with the lowest variance of 6.02\% when working with a Deep Research grounder. Our Jupyter Notebook grounder shows strong cost-effectiveness that achieves a close 70.11\% accuracy with 90.35\% less cost and 52.85\% less time. Analytica also exhibits highly noise-resilient and stable performance growth as the analysis depth increases, with a near-linear time complexity, as well as good adaptivity to open-weight LLMs and scientific domains.

Chain-of-Thought (CoT) has emerged as an effective paradigm to enhance the reasoning ability of large language models (LLMs) in complex tasks. However, existing approaches still face two major challenges: (1) the lack of a global mechanism to integrate and interact across diverse reasoning hypotheses, and (2) the absence of structured analysis techniques to filter redundancy and extract salient reasoning features. To address these challenges, we propose GHS-TDA (Global Hypothesis Space with Topological Data Analysis), a two-stage reasoning framework that achieves synergistic enhancement through global information integration and topological feature analysis. Specifically, (i) Global Hypothesis Space (GHS) constructs a semantically enriched global hypothesis graph via agenda-driven multi-agent interactions, integrating diverse hypotheses and their semantic relations; (ii) Topological Data Analysis (TDA) applies persistent homology to extract multi-scale topological features, identify stable connected components and self-consistent loops, and derive a redundancy-free reasoning skeleton chain. GHS-TDA preserves reasoning diversity while leveraging topological stability to achieve self-aware convergence, ultimately producing high-confidence and interpretable reasoning paths. Experimental results show that GHS-TDA consistently outperforms existing methods across multiple benchmark datasets, demonstrating its effectiveness and competitiveness in complex reasoning scenarios.

Large Language Models have demonstrated superior reasoning capabilities by generating step-by-step reasoning in natural language before deriving the final answer. Recently, Geiping et al. introduced 3.5B-Huginn as an alternative to this paradigm, a depth-recurrent Transformer that increases computational depth per token by reusing a recurrent block in latent space. Despite its performance gains with increasing recurrences, this approach is inadequate for tasks demanding exploration and adaptivity, a limitation arising from its single, chain-like propagation mechanism. To address this, we propose a novel dynamic multi-branches routing approach for Huginn, termed as Mixture-of-Depth-Recurrent (MoDr) Transformer, which enables effective exploration of the solution space by shifting linear latent reasoning into a LoRA-based multi-branch dynamic relay mode with a learnable hard-gate routing. Meanwhile, we introduce an auxiliary-loss-free load balancing strategy to mitigate the potential routing collapse. Our empirical results reveal that MoDr achieves average accuracy improvements of +7.2% and +2.48% over the original Huginn model and its fine-tuned variant, respectively, across various mathematical reasoning benchmarks and improvements of +21.21% and +1.52% on commonsense reasoning benchmarks.

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@$1$ and surpass them for pass@$32$, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

Process reward models (PRMs) have demonstrated significant efficacy in enhancing the mathematical reasoning capabilities of large language models (LLMs) by leveraging test-time scaling (TTS). However, while most PRMs exhibit substantial gains in mathematical domains, the scarcity of domain-specific training data and knowledge-based learning patterns limits their generalization ability when faced with other domains. To address this limitation, we shift the learning objective from verifying domain-specific knowledge to modeling domain-agnostic logical flow. Centering on \textit{contextual coherence} between chain-of-thought (CoT) steps, our approach is realized through a novel data annotation and training framework, which enhances the model's generalization capabilities across diverse domains. For instance, our resulting model, \textbf{ContextPRM}, achieves a notable 6.5\% average accuracy improvement over the majority voting baseline via weighted majority voting across nine non-mathematical domains in MMLU-Pro, including law, history, and philosophy, significantly surpassing the 2.2\% improvement from VersaPRM and 0.5\% gains from other mathematics-focused PRMs, demonstrating consistent performance across both mathematical and non-mathematical domains.

The dominant paradigm for training large reasoning models starts with pre-training using next-token prediction loss on vast amounts of data. Reinforcement learning, while powerful in scaling reasoning, is introduced only as the very last phase of post-training, preceded by supervised fine-tuning. While dominant, is this an optimal way of training? In this paper, we present RLP, an information-driven reinforcement pretraining objective, that brings the core spirit of reinforcement learning---exploration---to the last phase of pretraining. The key idea is to treat chain-of-thought as an exploratory action, with rewards computed based on the information gain it provides for predicting future tokens. This training objective essentially encourages the model to think for itself before predicting what comes next, thus teaching an independent thinking behavior earlier in the pretraining. More concretely, the reward signal measures the increase in log-likelihood of the next token when conditioning on both context and a sampled reasoning chain, compared to conditioning on context alone. This approach yields a verifier-free dense reward signal, allowing for efficient training for the full document stream during pretraining. Specifically, RLP reframes reinforcement learning for reasoning as a pretraining objective on ordinary text, bridging the gap between next-token prediction and the emergence of useful chain-of-thought reasoning. Pretraining with RLP on Qwen3-1.7B-Base lifts the overall average across an eight‑benchmark math‑and‑science suite by 19%. With identical post‑training, the gains compound, with the largest improvements on reasoning‑heavy tasks such as AIME25 and MMLU‑Pro. Applying RLP to the hybrid NVIDIA-Nemotron-Nano-12B-v2-Base increases the overall average from 42.81% to 61.32% and raises the average on scientific reasoning by 23%, demonstrating scalability across architectures and model sizes.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a crucial paradigm for incentivizing reasoning capabilities in Large Language Models (LLMs). Due to vast state-action spaces and reward sparsity in reasoning tasks, existing methods often struggle with deficient exploration and poor sample efficiency. In the paper, we propose **DIVER** (**D**iversity-**I**ncentivized Exploration for **V**ersatil**E** **R**easoning), an innovative framework that highlights the pivotal role of global sequence-level diversity to incentivize deep exploration for versatile reasoning. We first conduct a primary empirical study to reveal a strong positive correlation between global diversity and reasoning capacity. Building on this insight, we introduce global diversity incentives as an intrinsic reward to promote deep exploration in a semantically structured space. Incorporating the intrinsic reward, we develop a potential-based reward shaping mechanism to preserve optimal policy invariance and design simple heuristics to mitigate possible reward hacking. Experimental results show that DIVER outperforms competitive RLVR baselines with various exploration strategies on both in-domain and out-of-domain tasks, excelling in both Pass@1 and Pass@k evaluations. Our code is available at https://github.com/NJU-RL/DIVER.

Self-evolving Large Language Models (LLMs) offer a scalable path toward super-intelligence by autonomously generating, refining, and learning from their own experiences. However, existing methods for training such models still rely heavily on vast human-curated tasks and labels, typically via fine-tuning or reinforcement learning, which poses a fundamental bottleneck to advancing AI systems toward capabilities beyond human intelligence. To overcome this limitation, we introduce R-Zero, a fully autonomous framework that generates its own training data from scratch. Starting from a single base LLM, R-Zero initializes two independent models with distinct roles, a Challenger and a Solver. These models are optimized separately and co-evolve through interaction: the Challenger is rewarded for proposing tasks near the edge of the Solver capability, and the Solver is rewarded for solving increasingly challenging tasks posed by the Challenger. This process yields a targeted, self-improving curriculum without any pre-existing tasks and labels. Empirically, R-Zero substantially improves reasoning capability across different backbone LLMs, e.g., boosting the Qwen3-4B-Base by +6.49 on math-reasoning benchmarks and +7.54 on general-domain reasoning benchmarks.