ICLR 2026 Papers

Chain-of-thought (CoT) prompting is a de-facto standard technique to elicit reasoning-like responses from large language models (LLMs), allowing them to spell out individual steps before giving a final answer. While the resemblance to human-like reasoning is undeniable, the driving forces underpinning the success of CoT reasoning still remain largely unclear. In this work, we perform an in-depth analysis of CoT traces originating from competition-level mathematics questions, with the aim of better understanding how, and which parts of CoT actually contribute to the final answer. To this end, we introduce the notion of a \textit{potential}, quantifying how much a given part of CoT increases the likelihood of a correct completion. Upon examination of reasoning traces through the lens of the potential, we identify surprising patterns including (1) its often strong non-monotonicity (due to reasoning tangents), (2) very sharp but sometimes tough to interpret spikes (reasoning insights and jumps) as well as (3) at times lucky guesses, where the model arrives at the correct answer without providing any relevant justifications before. While some of the behaviours of the potential are readily interpretable and align with human intuition (such as insights and tangents), others remain difficult to understand from a human perspective. To further quantify the reliance of LLMs on reasoning insights, we investigate the notion of CoT transferability, where we measure the potential of a weaker model under the partial CoT from another, stronger model. Indeed aligning with our previous results, we find that as little as 20% of partial CoT can ``unlock'' the performance of the weaker model on problems that were previously unsolvable for it, highlighting that a large part of the mechanics underpinning CoT are transferable.

Previous work shows that the chain of continuous thought (continuous CoT) improves the reasoning capability of large language models (LLMs) by enabling implicit parallel thinking, and a subsequent work provided theoretical insight by showing that a two-layer transformer equipped with continuous CoT can efficiently solve directed graph reachability by maintaining a superposition of multiple reasoning traces in the continuous thought. However, it remains unclear how the superposition mechanism is naturally learned from gradient-based training methods. To fill this gap, we theoretically analyze the training dynamics of a simplified two-layer transformer on the directed graph reachability problem to unveil how the superposition mechanism emerges during training in two training stages -- (i) a *thought-generation* stage that autoregressively expands the continuous thought, and (ii) a *prediction* stage that converts the thought into the final answer. Our analysis reveals that during training using continuous thought, the index-matching logit, an important quantity which reflects the strength of the model's local search ability, will first increase and then remain bounded under mild assumptions. The bounded index-matching logit effectively balances exploration and exploitation during the reasoning process: the model will exploit local problem structures to identify plausible search traces, and assign comparable weights to multiple such traces to explore when it is uncertain about which solution is correct, which results in superposition. Our experimental results tracking the growth of logits further validate our theory.

Growing concerns over the theft and misuse of Large Language Models (LLMs) underscore the need for effective fingerprinting to link a model to its original version and detect misuse. We define five essential properties for a successful fingerprint: Transparency, Efficiency, Persistence, Robustness, and Unforgeability. We present a novel fingerprinting framework that provides verifiable proof of ownership while preserving fingerprint integrity. Our approach makes two main contributions. First, a "chain and hash" technique that cryptographically binds fingerprint prompts to their responses, preventing collisions and enabling irrefutable ownership claims. Second, we address a realistic threat model in which instruction-tuned models' output distribution can be significantly altered through meta-prompts. By incorporating random padding and varied meta-prompt configurations during training, our method maintains robustness even under significant output style changes. Experiments show that our framework securely proves ownership, resists both benign transformations (e.g., fine-tuning) and adversarial fingerprint removal, and extends to fingerprinting LoRA adapters.

Recently, OpenAI (2025) showed that training against a chain of thought (CoT) monitor can cause obfuscated CoTs, which contain bad behavior the monitor cannot detect. They proposed to keep CoTs monitorable by training only against output monitors that do not have access to CoT. We show that such training can still cause obfuscated CoTs via two mechanisms. First, when a model is trained to produce a safe-looking output, that model may generalize to making its CoTs look safe. Second, since later tokens are conditioned on earlier ones, safe‑looking CoTs may increase the likelihood of safe outputs, causing safe-looking CoTs to be reinforced. We introduce two mitigations to address these two issues, which achieve a Pareto improvement in terms of monitorability and task performance compared to regular training. To our knowledge, we are the first to identify and mitigate these problems. Our work implies that preserving CoT monitorability is more difficult than previously thought; we suggest practical guidelines for AI developers to maintain monitorable CoTs.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases—thinking and solution—with independently allocated budgets. At test time, Elastic Reasoning prioritizes the completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale. Code is available in the supplementary material.

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.

While large reasoning models have shown remarkable ability to generate long chains-of-thought (CoTs) in English, we still lack understanding of how these long-form reasoning abilities transfer to the vast majority of the world’s languages. In this work, we systematically investigate four key stages of model development–scaling, pretraining, post-training, and inference–to understand how long CoT capabilities extend beyond English. We compare two reasoning settings across nine non-English target languages: En-CoT, where models process target-language inputs, but reason in English; and Target-CoT, where models both process inputs and generate long CoTs in the target language. We find that scaling reasoning model size improves multilingual task performance in En-CoT, but Target-CoT performance lags behind. This gap widens for tasks requiring long, multi-step CoTs such as mathematical reasoning. Shifting to pretraining, we find that adding a specialized reasoning stage enhances En-CoT performance but degrades Target-CoT, whereas broad multilingual pretraining improves both modes simultaneously. Given the scarcity of high-quality reasoning traces in languages other than English, we explore synthetic data curation approaches for post-training. We demonstrate that fine-tuning on reasoning traces automatically translated from gold English traces outperforms fine-tuning on target-language traces distilled from large reasoning models. Finally, we report disparities in inference efficiency between languages and uncover language-specific failure modes in CoTs. We release models, datasets, and code to foster further research.