CoT Distillation

CoT: Chain-of-Thought

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4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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May 29, 2026cs.CL

Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

Yuxuan Jiang, Francis Ferraro

University of Maryland, Baltimore County

CoT Distillation Language Model Distillation On-Policy Distillation Teacher-Student Learning Knowledge Distillation

May 29, 2026cs.CL

Your Teacher Can't Help You Here: Combating Supervision Fidelity Decay in On-Policy Distillation

On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, \textbf{Supervision Fidelity Decay (SFD)}: as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce \textbf{Lookahead Group Reward (\ours{})}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, \ours{} evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, \ours{} improves mean@8 by \textbf{2.57} points over OPD for a 7B student, with gains increasing in longer-generation and reaching +\textbf{4.92} points on AIME-26 at 39k tokens.

Yanjiang Liu, Jie Lou, Xinyan Guan +7

University of Chinese Academy of Sciences · 2Chinese Information Processing Laboratory Institute of Software, Chinese Academy of Sciences 2University of Chinese Academy of Sciences, Beijing, China · 3Xiaohongshu

CoT Distillation Language Model Distillation On-Policy Distillation Teacher-Student Learning RL Fine-Tuning

May 28, 2026cs.LG

LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor

ρ

, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a

χ^2

-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Tianrun Yu, Kaixiang Zhao, Chih-Chun Chen +5

Brigham Young University · The Pennsylvania State University · University of North Carolina at Chapel Hill

CoT Distillation Language Model Distillation Teacher-Student Learning Data-Efficient Learning

May 27, 2026cs.AI

Better Accuracies, Worse Reasoning: A Step-Level Audit of Medical Chain-of-Thought Distillation

Chain-of-thought (CoT) distillation trains a smaller model to imitate a teacher's reasoning trace, but it is typically evaluated by final-answer metrics including accuracy. We ask whether gains in answer quality are accompanied by improvements in the trace. In medical QA, where short answer options can leave a richer clinical justification under-specified, a Qwen3-8B student distilled from a DeepSeek-V3-family teacher improves on MedQA-USMLE answer metrics (SC@64 74.7% to 84.4%; expected calibration error (ECE) 0.096 to 0.034). Yet under a Kimi-K2.6 style-blind LLM-judge audit, its error rate over non-abstained steps rises from 30.6% to 50.3%. In this primary medical setting, answer quality and trace factuality move in opposite directions. This before--after pattern persists across evaluators, teacher strengths, student scales and families, medical benchmarks, and style, segmentation, and answer-correctness controls. A 150-step blinded audit by a clinical expert reproduces the same ordering. Boundary checks narrow the scope of the claim: the risk appears when a compact answer under-constrains the rationale and a capable student can imitate expert-like form without reliably grounding each local claim. Standard answer metrics and aggregate hedging rates do not reveal the shift. When such traces are released or reused, answer-level metrics alone are insufficient.

Zhaoyang Jiang, Xuanqi Peng, Fei Teng +5

School of Health & Wellbeing, University of Glasgow, Glasgow, UK · Department of Respiratory and Critical Care Medicine, Shanghai Sixth People’s Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China · School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China +1

CoT Distillation CoT Evaluation Clinical QA Medical Reasoning Teacher-Student Learning

May 27, 2026cs.IR

Generative Spatiotemporal Intent Sequence Recommendation via Implicit Reasoning in Amap

Real-world user behavior rarely consists of isolated actions; instead, it often forms intent flows governed by spatiotemporal dependencies. To provide integrated service recommendations, we focus on the task of Generative Spatiotemporal Intent Sequence Recommendation (GSISR), which aims to generate intent sequences that are logically coherent and physically executable within complex spatiotemporal contexts. While LLMs offer strong reasoning potential for GSISR, direct industrial deployment is limited by high inference latency and context-mismatched or physically infeasible plans. To address these challenges, we propose a generative framework, GPlan, that internalizes LLM reasoning into lightweight models through two components. First, to enable reasoning under strict latency constraints, we introduce Progressive Implicit CoT Distillation, which compresses explicit reasoning processes into reserved latent tokens, allowing small models to inherit complex planning logic without generating long reasoning text. Second, to address the disconnect between general knowledge and real-world constraints, we design Spatiotemporal Counterfactual DPO. By aligning the model with counterfactual context-plan pairs, we improve sensitivity to spatiotemporal context and reduce context-mismatched plans. Offline experiments and online A/B testing demonstrate that our approach improves sequence coherence and context responsiveness. Our implementation and the anonymized GSISR dataset are available at https://github.com/alibaba/GPlan.

Sicong Wang, Ruiting Dong, Yue Liu +7

AMAP, Alibaba Group, Beijing, China

Spatiotemporal Reasoning CoT Distillation Large Language Model-Based Recommendation Generative Recommendation

May 20, 2026cs.LG

When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.

Xiaogeng Liu, Xinyan Wang, Yingzi Ma +2

1Johns Hopkins University · University of Wisconsin–Madison · 3Nanyang Technological University

CoT Distillation On-Policy Self-Distillation Mathematical Reasoning Language Model Distillation Teacher-Student Learning Knowledge Distillation

May 19, 2026cs.CL

Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation

Large language models (LLMs) have achieved remarkable success in complex reasoning tasks via long chain-of-thought (CoT), yet their immense computational overhead hinders real-world deployment. LLM reasoning distillation addresses this by transferring reasoning capabilities from formidable teacher models to compact student models. However, existing distillation paradigms face a fundamental dilemma. Typical off-policy distillation strictly utilizes teacher-generated golden trajectories, suffering from an exposure bias due to the mismatch between training distributions and student-generated inference contexts, which leads to error cascades in long CoT reasoning. To address this, on-policy distillation allows students to explore their own trajectories, but we demonstrate that it inherently introduces a reciprocal reversed exposure bias: the teacher model also struggles to provide positive guidance when conditioned on student-generated sub-optimal contexts. To resolve this dual exposure biases problem, we propose Monitoring Trajectories and Backtracking when it strays (MOTAB), a new LLM reasoning distillation pipeline. Specifically, MOTAB dynamically monitors the student's on-policy generation against an adaptive safety boundary. When the generation strays and exceeds this threshold, MOTAB backtracks to the last safe state and leverages teacher intervention to correct the course. This approach inherently tolerates minor student errors to mitigate exposure bias, while preventing sub-optimal contexts to circumvent reversed exposure bias. Extensive experiments on the LIMO-v2 and AceReason datasets demonstrate that MOTAB effectively alleviates the dual exposure biases, yielding a roughly 3% average performance improvement in reasoning tasks.

Bing Wang, Shaotian Yan, Chen Shen +7

College of Computer Science and Technology, Jilin University · Key Laboratory of Symbolic Computation and Knowledge Engineering, MoE, Jilin University · Tongyi Lab, Alibaba Group +3

CoT Distillation Language Model Distillation On-Policy Distillation

May 13, 2026cs.CL

Distribution Corrected Offline Data Distillation for Large Language Models

Distilling reasoning traces from strong large language models into smaller ones is a promising route to improve intelligence in resource-constrained settings. Existing approaches face a fundamental trade-off: offline distillation from teacher-generated traces provides high-quality, sample-efficient supervision but suffers from distributional drift: during training, the student model conditions on teacher-generated prefixes, whereas during inference the student autoregresses on self-generated prefixes, leading to compounding errors over long reasoning trajectories. Meanwhile, on-policy or self-distillation methods better match the student's inference-time distribution, but require costly online sampling and often produce low-quality traces in early training. We propose a principled offline reasoning distillation framework that preserves the efficiency and supervision quality of offline teacher-generated data while correcting teacher-student distribution drift. It adaptively emphasizes teacher supervision that is better aligned with the student's on-policy distribution. Evaluations on mathematical reasoning benchmarks of GSM8K, MATH, MATH500, and harder held-out competition-style tasks, including AMC, AIME, and OlympiadBench, show that our method improves reasoning accuracy over prior offline distillation algorithms and yields more stable reasoning traces while preserving instruction-following capabilities. Our work shows that lightweight, distribution-correction-aware training can substantially strengthen offline reasoning distillation without online rollouts.

Yumeng Zhang, Zhengbang Yang, Yevin Nikhel Goonatilake +1

George Mason University, Fairfax, VA, USA

CoT Distillation Efficient Language Model Reasoning Language Model Distillation Teacher-Student Learning Knowledge Distillation

May 13, 2026cs.CL

GateKD: Confidence-Gated Closed-Loop Distillation for Robust Reasoning

Distilling multi-step reasoning abilities from large language models (LLMs) into compact student models remains challenging due to noisy rationales, hallucinated supervision, and static teacher-student interactions. Existing reasoning distillation methods, including mentor-based approaches, predominantly operate in an open-loop manner, implicitly assuming uniform teacher reliability and consequently propagating erroneous intermediate reasoning. We propose GateKD, a confidence-gated closed-loop distillation framework that enables robust reasoning transfer by treating the teacher as a dynamic gatekeeper rather than a static oracle. GateKD introduces three complementary mechanisms: (i) confidence-gated soft supervision that selectively distills reliable predictive signals, (ii) gated hidden-state evolution that aligns intermediate representations only when teacher confidence is high, and (iii) reliability-filtered attention distillation that preserves stable reasoning structures while suppressing noisy patterns. These components jointly form a closed feedback loop in which teacher confidence continuously modulates the distillation process, reducing hallucination transfer and stabilizing student reasoning. Extensive experiments across commonsense, logical, and symbolic reasoning benchmarks, using T5 and Flan-T5 backbones of varying sizes, demonstrate that GateKD consistently outperforms strong open-loop distillation baselines. Notably, GateKD yields substantial gains in logical and symbolic reasoning, remains robust under low-resource distillation settings, and shows clear performance degradation when any gating component is removed. Our results highlight that confidence-gated closed-loop supervision is critical for building reliable and scalable small reasoning models.

Kasidit Sermsri, Teerapong Panboonyuen

†Chulalongkorn University · ‡MARSAIL · §PBYAIL (Panboonyuen AI Lab)

CoT Distillation Language Model Distillation Uncertainty-Aware Knowledge Distillation Language Model Robustness Knowledge Distillation LLM Reasoning

May 12, 2026cs.CV

Hide to See: Reasoning-prefix Masking for Visual-anchored Thinking in VLM Distillation

Recent think-answer approaches in VLMs, such as Qwen3-VL-Thinking, boost reasoning performance by leveraging intermediate thinking steps before the final answer, but their computational cost becomes substantial, especially for larger VLMs. To distill such capabilities into compact think-answer VLMs, a primary objective is to improve the student's ability to utilize visual evidence throughout its reasoning trace, as long think-answer traces suffer from visual forgetting issues. To this end, we introduce a novel think-answer distillation framework that encourages the student to anchor its thinking on visual information by masking the student's salient reasoning prefixes. To compensate for such masked textual cues, the student is encouraged to rely more on visual evidence as an alternative source of information during distillation. Our masking strategies include: 1) token-wise salient reasoning-prefix masking, which masks high-influence reasoning prefixes selectively for each next-token prediction, and 2) self-paced masking budget scheduling, which gradually increases the masking scale according to distillation difficulty, measured by the discrepancy between teacher--student distributions. In the distillation phase, the student is guided by our salient reasoning-prefix mask, which blocks both future tokens and salient reasoning cues, in place of the standard causal mask used for auto-regressive language modeling. Experimental results show that our approach outperforms recent open-source VLMs, VLM distillation, and self-distillation methods on multimodal reasoning benchmarks, while further analyzes confirm enhanced visual utilization along the student thinking process.

Seonghoon Yu, Dongjun Nam, Byung-Kwan Lee +1

1KAIST · 3POSTECH · 2NVIDIA

Cross-Modal Knowledge Distillation CoT Distillation VLM Distillation VLM Reasoning

May 10, 2026cs.CV

On-Policy Distillation with Best-of-N Teacher Rollout Selection

On-policy distillation (OPD), which supervises a student on its own sampled trajectories, has emerged as a data-efficient post-training method for improving reasoning while avoiding the reward dependence of reinforcement learning and the catastrophic forgetting often observed in standard supervised fine-tuning. However, standard OPD typically computes teacher supervision under noisy student-generated contexts and often relies on a single stochastic teacher rollout per prompt. As a result, the supervision signal can be high-variance: the sampled teacher trajectory can be incorrect, uninformative, or poorly matched to the student's current reasoning behavior. To address this limitation, we propose BRTS, a Best-of-N Rollout Teacher Selection framework for on-policy distillation. BRTS augments standard student-context OPD with a teacher-context supervision branch constructed from the curated teacher trajectory. Rather than distilling from the first sampled teacher rollout, BRTS samples a small pool of teacher trajectories and selects the auxiliary trajectory using a simple priority rule: correctness first, student alignment second. When multiple correct teacher trajectories are available, BRTS chooses the one most aligned with the student's current behavior; when unconditioned teacher samples fail on harder prompts, it invokes a ground-truth-conditioned recovery step to elicit a natural derivation. The selected trajectory is then used to provide reliable teacher-context supervision inside the OPD loop, augmented with an auxiliary loss on the teacher trajectory. Experiments on AIME 2024, AIME 2025, and AMC 2023 show that BRTS improves over standard OPD on challenging reasoning benchmarks, with the largest gains on harder datasets. Our code is available at https://github.com/BWGZK-keke/BRTS.

Ke Zhang, Yunjie Tian, Dongdi Zhao +4

Johns Hopkins University · TikTok · University of California, San Diego +1

CoT Distillation Best-of-N Sampling Mathematical Reasoning Language Model Distillation On-Policy Distillation Teacher-Student Learning

May 10, 2026cs.CV

LiteMedCoT-VL: Parameter-Efficient Adaptation for Medical Visual Question Answering

The reasoning gap between large and compact vision-language models (VLMs) limits the deployment of medical AI on portable clinical devices. Compact VLMs of 2--4B parameters can run on resource-constrained hardware but lack the multi-step reasoning capacity needed for interpretable clinical decision support. Existing knowledge distillation methods transfer answers without the reasoning process behind them. Medical visual question answering (VQA) serves as a testbed for this problem, as it requires models to integrate visual evidence with clinical knowledge through structured reasoning chains. We introduce LiteMedCoT-VL, a pipeline that transfers chain-of-thought reasoning from a 235B teacher model to 2B student models through LoRA-based fine-tuning on explanation-enriched training data. All inference is conducted without image captions by default, simulating the clinical scenario in which a physician interprets a medical image directly without an accompanying radiology report. On the PMC-VQA benchmark, LiteMedCoT-VL achieves 64.9% accuracy, exceeding the zero-shot Qwen3-VL-4B baseline of 53.9% by 11.0 percentage points and outperforming all published baselines. This result indicates that a 2B model with reasoning distillation can match or exceed models with twice the parameters. Visual grounding analysis shows that the model relies on image content rather than exploiting textual priors. Our code is publicly available at https://anonymous.4open.science/r/LiteMedCoT-VL.

Runze Ma, Shunbo Jia, Haonan Lyu +2

School of Information Technology Monash University Malaysia · Faculty of Innovation Engineering Macau University of Science and Technology · Department of Bioelectronics Faculty of Biomedical Engineering Shenzhen University of Advanced Technology +1

CoT Distillation Healthcare Medical VQA Medical VLMs VLM Reasoning Knowledge Distillation

May 8, 2026cs.CL

Structural Rationale Distillation via Reasoning Space Compression

When distilling reasoning from large language models (LLMs) into smaller ones, teacher rationales for similar problems often vary wildly in structure and strategy. Like a chef who makes the same dish differently each time, this inconsistency burdens the student with noisy supervision that is hard to internalize. We propose Distillation through Reasoning Path Compression (D-RPC), which constrains the teacher to follow a compact, dynamically maintained bank of reusable high-level reasoning paths. For each training question, D-RPC retrieves the most relevant path and conditions the teacher to follow it, producing rationales that are consistent across similar problems yet diverse enough to cover different problem types. A PAC-Bayes analysis formalizes the resulting trade-off between bank size and coverage: smaller banks reduce supervision entropy but risk coverage gaps, and the generalization bound identifies an optimal intermediate size confirmed by our ablations. Across five math and commonsense reasoning benchmarks with two student models, D-RPC consistently outperforms chain-of-thought distillation, freeform rationale generation, direct distillation, and structured-supervision baselines, while using fewer tokens than template-heavy alternatives.

Jialin Yang, Jiankun Wang, Jiajun Wu +3

University of Calgary · Calgary, Canada · University of Michigan +1

CoT Distillation Structured Reasoning Teacher-Student Learning Knowledge Distillation CoT Compression LLM Reasoning

May 4, 2026cs.AI

Distilling Long-CoT Reasoning through Collaborative Step-wise Multi-Teacher Decoding

Distilling large reasoning models is essential for making Long-CoT reasoning practical, as full-scale inference remains computationally prohibitive. Existing curation-based approaches select complete reasoning traces post-hoc, overlooking collaboration among heterogeneous teachers and lacking dynamic exploration, which leads to redundant sampling and missed complementary reasoning. We introduce CoRD, a collaborative multi-teacher decoding framework that performs step-wise reasoning synthesis guided by predictive perplexity-based scoring and beam search. This enables heterogeneous LRMs to jointly construct coherent reasoning trajectories while efficiently preserving diverse, high-potential hypotheses. Experiments show that CoRD produces higher-quality reasoning data and achieves near teacher-level student performance with fewer, structured supervision signals, without substantial efficiency overhead. CoRD further generalizes well to out-of-domain and open-ended settings. The dataset and model are available at https://github.com/DISL-Lab/CoRD.

Taewon Yun, Jisu Shin, Jeonghwan Choi +2

KAIST · UNIST

CoT Distillation Efficient Language Model Reasoning Multi-Teacher Knowledge Distillation Teacher-Student Learning Multi-LLM Collaboration Large Reasoning Models

Apr 25, 2026cs.CR

Hiding in Plain Sight: Detectability-Aware Antidistillation of Reasoning Models

Distillation via sampling reasoning traces exposes closed-source frontier models to adversarial third parties who can bypass their guardrails and misappropriate their capabilities. Antidistillation methods aim to address this by poisoning reasoning traces to hinder student model learning while preserving teacher performance. However, current methods overlook detectability, both semantic and syntactic, which erodes trust in the teacher's outputs and signals the defense's presence to adversaries. We address this gap by formulating antidistillation as a Stackelberg game whose constraint set explicitly encodes detectability, and show that perturbing sparingly offers an effective, less detectable alternative to poisoning the full trace. Drawing on mechanistic interpretability, we identify thought anchors, sentences with disproportionate counterfactual influence on model outputs, as a principled sparse target: critical to reasoning yet minimally detectable. We instantiate this in TraceGuard, a training-free, black-box proof-of-concept that locates thought anchors via branching-token detection and poisons them to degrade student distillation while preserving trace coherence.

Max Hartman, Vidhata Jayaraman, Moulik Choraria +2

University of Illinois Urbana-Champaign · Carnegie Mellon University · Stony Brook University

CoT Distillation Teacher-Student Learning Knowledge Distillation Reasoning Trace Analysis

Apr 17, 2026cs.CL

Improving Reasoning Capabilities in Small Models through Mixture-of-Layers Distillation with Stepwise Attention on Key Information

The significant computational demands of large language models have increased interest in distilling reasoning abilities into smaller models via Chain-of-Thought (CoT) distillation. Current CoT distillation methods mainly focus on transferring teacher-generated rationales for complex reasoning to student models. However, they do not adequately explore teachers' dynamic attention toward critical information during reasoning. We find that language models exhibit progressive attention shifts towards key information during reasoning, which implies essential clues for drawing conclusions. Building on this observation and analysis, we introduce a novel CoT distillation framework that transfers the teacher's stepwise attention on key information to the student model. This establishes structured guidance for the student's progressive concentration on key information during reasoning. More importantly, we develop a Mixture of Layers module enabling dynamic alignment that adapts to different layers between the teacher and student. Our method achieves consistent performance improvements across multiple mathematical and commonsense reasoning datasets. To our knowledge, it is the first method to leverage stepwise attention within CoT distillation to improve small model reasoning.

Yao Chen, Jiawei Sheng, Wenyuan Zhang +1

Institute of Information Engineering, Chinese Academy of Sciences · School of Cyber Security, University of Chinese Academy of Sciences

CoT Distillation Small Language Models Transfer Learning Language Model Distillation Attention Mechanisms Knowledge Distillation

Apr 10, 2026cs.LG

Revisiting the Capacity Gap in Chain-of-Thought Distillation from a Practical Perspective

Chain-of-thought (CoT) distillation transfers reasoning behaviors from a strong teacher to a smaller student, but prior work reports a capacity gap: distillation may fail when the teacher-student capability mismatch is large. We revisit the capacity gap from a practical perspective by re-examining commonly used experimental settings. Notably, we find that CoT distillation often degrades performance compared to the student's pre-distillation baseline, and that some settings used in prior work, while suitable for establishing the capacity gap as a phenomenon, do not reflect realistic deployment scenarios. Complementing prior work that establishes the capacity gap, we evaluate its practical impact under more realistic settings and find that it does not consistently dominate; stronger teachers tend to be preferable when candidate teachers differ substantially in performance. Our results offer practical guidance for selecting teacher-student pairs in CoT distillation.

Tokio Kajitsuka, Ukyo Honda, Sho Takase

The University of Tokyo, Tokyo, Japan · CyberAgent, Tokyo, Japan

CoT Distillation Reasoning Distillation Teacher-Student Learning Knowledge Distillation

Mar 20, 2026cs.AI

Grounded Chess Reasoning in Language Models via Master Distillation

Language models often lack grounded reasoning capabilities in specialized domains where training data is scarce but bespoke systems excel. We introduce a general framework for distilling expert system reasoning into natural language chain-of-thought explanations, enabling compact models to acquire domain expertise and the ability to generate faithful, grounded explanations. Rather than distilling only final outputs, we capture the full reasoning process, transforming opaque expert computations into transparent, step-by-step explanations. We demonstrate this approach in chess, a canonical reasoning domain where language models continue to underperform. Our 4B parameter model, C1, advances from a near-zero baseline to 48.1% accuracy, outperforming all open-source models and most frontier proprietary systems. Notably, C1 surpasses its distillation teacher and generates solutions in two orders of magnitude fewer tokens than baselines. Unlike prior neural chess approaches that predict only best moves, C1 generates explainable solutions revealing strategic reasoning. Our pipeline combines supervised fine-tuning and reinforcement learning with theme-balanced data sampling for comprehensive tactical coverage. Master Distillation demonstrates how to inject expert-level knowledge into compact models for under-optimized domains, offering a recipe for unlocking RLVR where LLMs lack sufficient base capabilities.

Zhenwei Tang, Qianfeng Wen, Seth Grief-Albert +4

Department of Computer Science, University of Toronto · Queen’s University · Coolwei AI Lab

LLM Grounding CoT Distillation Language Model Distillation Chess LLM Reasoning

Mar 11, 2026cs.AI

HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation

Distilling reasoning capabilities from Large Reasoning Models (LRMs) into smaller models is typically constrained by the limitations of rejection sampling. Standard methods treat the teacher as a static filter, discarding complex "corner-case" problems where the teacher fails to explore valid solutions independently, thereby creating an artificial "Teacher Ceiling" for the student. In this work, we propose Hindsight Entropy-Assisted Learning (HEAL), an RL-free framework designed to bridge this reasoning gap. Drawing on the educational theory of the Zone of Proximal Development (ZPD), HEAL synergizes three core modules: (1) Guided Entropy-Assisted Repair (GEAR), an active intervention mechanism that detects critical reasoning breakpoints via entropy dynamics and injects targeted hindsight hints to repair broken trajectories; (2) Perplexity-Uncertainty Ratio Estimator (PURE), a ratio-based filtering heuristic that reduces high-anomaly shortcut-like rationales; and (3) Progressive Answer-guided Curriculum Evolution (PACE), a three-stage distillation strategy that organizes training from foundational alignment to hard-case adaptation. Extensive experiments on multiple benchmarks demonstrate that HEAL significantly outperforms traditional SFT distillation and other baselines.

Wenjing Zhang, Jiangze Yan, Jieyun Huang +7

Data Science & AI Research Institute, China Unicom · Unicom Data Intelligence, China Unicom

CoT Distillation Language Model Distillation LLM Reasoning Large Reasoning Models

Mar 5, 2026cs.LG

CRISP: Compressed Reasoning via Iterative Self-Policy Distillation

Reasoning models often generate far more tokens than a task requires, which raises inference cost and can compound errors. We introduce CRISP (Compressed Reasoning via Iterative Self-Policy Distillation), an on-policy self-distillation method that teaches a model to reason more concisely by distilling its own concise behavior back into itself. The method uses a single idea: condition the same model on a "be concise" instruction to obtain teacher logits, then minimize the per-token reverse KL divergence between the student and this teacher on the student's own rollouts. It requires no ground-truth answers, no token budgets, and no difficulty estimators. The reverse-KL objective is naturally difficulty-adaptive: it compresses easy problems aggressively while preserving the reasoning steps that hard problems require. On Qwen3-14B, CRISP cuts reasoning length by up to 56% on MATH-500 and 38% on the harder AIME 2024, while improving MATH-500 accuracy by up to 3.3 points over the base model and holding AIME 2024 accuracy within about one point. This behavior generalizes across model sizes and families: Qwen3-8B shows the same compression with accuracy preserved, and DeepSeek-R1-Distill-Llama-8B improves accuracy on all five benchmarks while shortening its responses. General capabilities are preserved across all three models. Code is available at https://github.com/HJSang/OPSD_Reasoning_Compression.

Hejian Sang, Yuanda Xu, Zhengze Zhou +3

CoT Distillation Efficient Language Model Reasoning On-Policy Distillation CoT Compression LLM Reasoning

Feb 16, 2026cs.CL

Measuring and Mitigating Post-hoc Rationalization in Reverse Chain-of-Thought Generation

Reverse Chain-of-Thought Generation (RCG) synthesizes reasoning traces from query-answer pairs, but it risks producing post-hoc rationalizations: when models can see the answer during generation, a systematic train-inference mismatch arises, because the visible answer shapes reasoning trajectories in ways that students cannot replicate without answer access during inference. We formalize this mismatch through a three-level measurement hierarchy: lexical, trajectory, and probabilistic anchoring, which capture surface token overlap, per-token generation dependence on the answer, and total information transmission from trace to answer, respectively. We analyze semantic suppression, the intuitive mitigation strategy that instructs models to ignore the answer, and find that it is counterproductive: while it reduces lexical overlap, it paradoxically increases trajectory anchoring--the per-token dependence of the generation process on the forbidden answer--consistent with ironic monitoring. We attribute this failure to active monitoring of the forbidden answer, which inadvertently deepens process-level dependence on it. To break this cycle, we propose Structural Skeleton-guided Reasoning (SSR), whose core contribution is to replace answer suppression with structural decoupling: SSR first generates a response-abstracted functional skeleton designed to limit direct answer encoding and then uses it as a structural target for full trace generation. Experiments across open-ended reasoning benchmarks show that SSR consistently mitigates anchoring, and that Distilled SSR (SSR-D), a distillation variant that internalizes skeleton-guided reasoning from teacher-generated traces, achieves up to 10% improvement over suppression baselines while mitigating out-of-distribution (OOD) degradation.

Guangyue Peng, Zongchao Chen, Wen Luo +9

State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University · Nanbeige Lab, BOSS Zhipin · University of Electronic Science and Technology of China

CoT Distillation CoT Reasoning Reasoning Trace Analysis

Feb 5, 2026cs.LG

BRIDGE: Bridging Reasoning In Distillation Gap Elimination via Structure-Aware Masking

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.

Bowen Yu, Sheng Zhang, Binhao Wang +8

1City University of Hong Kong · 2Mohamed Bin Zayed University of Artificial Intelligence

CoT Distillation Mathematical Reasoning Teacher-Student Learning CoT Compression

Feb 3, 2026cs.AI

Distilling LLM Reasoning into Graph of Concept Predictors

Deploying Large Language Models (LLMs) for discriminative workloads is often limited by inference latency, compute, and API costs at scale. Active distillation reduces these costs by querying an LLM oracle to train small discriminative students, but most pipelines distill only final labels, discarding intermediate reasoning signals and offering limited diagnostics of what reasoning is missing and where errors arise. We propose Graph of Concept Predictors (GCP), a reasoning-aware active distillation framework in which the teacher's reasoning is elicited as a directed acyclic graph of intermediate concepts and mirrored in the student. GCP enhances sample efficiency through a graph-aware acquisition strategy that weights per-concept uncertainty, gradient diversity, and coverage by node centrality. Additionally, it improves training stability and efficiency by performing targeted sub-module retraining, which attributes downstream loss to specific concept predictors and updates only the most influential modules. Experiments on eight NLP classification benchmarks demonstrate that GCP enhances performance under limited annotation budgets while yielding more interpretable and controllable training dynamics. Code is available at https://github.com/Ziyang-Yu/GCP.

Ziyang Yu, Liang Zhao

Department of Computer Science Emory University Atlanta, USA

CoT Distillation Active Learning Text Classification Language Model Distillation

Dec 24, 2025cs.CL

Distilling the Essence: Efficient Reasoning Distillation via Sequence Truncation

Distilling the capabilities from a large reasoning model (LRM) to a smaller student model often involves training on substantial amounts of reasoning data. However, knowledge distillation (KD) over lengthy sequences with prompt (P), chain-of-thought (CoT), and answer (A) sections makes the process computationally expensive. In this work, we investigate how the allocation of supervision across different sections (P, CoT, A) affects student performance. Our analysis shows that selective KD over only the CoT tokens can be effective when the prompt and answer information is encompassed by it. Building on this insight, we establish a truncation protocol to quantify computation-quality tradeoffs as a function of sequence length. We observe that beyond a specific length, longer training sequences provide marginal returns for downstream performance but require substantially higher memory and FLOPs. To this end, training on only the first

50\%

of tokens of every training sequence can retain, on average,

\approx91\%

of full-sequence performance on math benchmarks while reducing training time, memory usage, and FLOPs by about

50\%

each. Codes are available at https://github.com/weiruichen01/distilling-the-essence.

Wei-Rui Chen, Vignesh Kothapalli, Ata Fatahibaarzi +5

1The University of British Columbia · 2LinkedIn · 3Canada Research Chair in NLP and ML

CoT Distillation Selective Knowledge Distillation Efficient Language Model Reasoning Efficient Language Model Training Teacher-Student Learning Knowledge Distillation+2

Nov 14, 2025cs.CV

From Hindsight to Foresight: Self-Encouraged Hindsight Distillation for Knowledge-based Visual Question Answering

Knowledge-based Visual Question Answering (KBVQA) necessitates external knowledge incorporation beyond cross-modal understanding. Existing KBVQA methods either utilize implicit knowledge in multimodal large language models via in-context learning or explicit knowledge via retrieval augmented generation. However, their reasoning processes remain implicit, without explicit multi-step trajectories. To address this gap, we propose a Self-Encouraged Hindsight Distillation Reasoning (HinD) framework, aiming at eliciting reasoning ability inside the MLLM by constructing a Hindsight Teacher with privileged information to teach the Foresight Student. First, we construct the Hindsight Teacher by prompting the MLLM with the reasoning target as privileged information to complete the reasoning process, obtaining Hindsight-Zero training data. Then, the Foresight Student, without knowing the answer, learns the golden trajectories from Hindsight in two ways: (1) Hindsight Distillation Fine-Tuning to self-distill the Hindsight-Zero into a modularized Chain-of-Thought Generator and a Knowledge Generator for sequential steps and discrete facts generation, respectively; (2) Knowledge Encouragement Preference Optimization to encourage the under-confident but relevant knowledge inside the MLLM and suppress the over-confident but irrelevant one. Experiments on OK-VQA and A-OKVQA validate the effectiveness of HinD, showing that HinD with 7-8B MLLM achieves superior performance without commercial model APIs or retrieved knowledge.

Yu Zhao, Ying Zhang, Xuhui Sui +4

College of Computer Science, VCIP, DISSec, Nankai University, Tianjin, China · School of Software, Tiangong University, Tianjin, China · Shenzhen Campus of Sun Yat-sen University, Shenzhen, China +1

Visual Question Answering CoT Distillation Large Vision-Language Models VLM Reasoning Knowledge-Based VQA Knowledge Distillation

Sep 26, 2025cs.CL

Scale or Reason? A Compute-Equivalent Analysis of Reasoning Distillation

Distilling reasoning traces from strong teacher models has become the standard recipe for building capable small language models. Yet reasoning traces are 5-20

\times

longer than standard instruction fine-tuning (IFT) outputs, meaning every practitioner who chooses reasoning distillation implicitly forgoes training a larger IFT model on the same compute budget. Whether this trade-off is worthwhile remains unaddressed. We study it with a controlled experiment: a single teacher generates paired IFT and reasoning outputs for identical prompts by toggling only its reasoning mode, isolating supervision format as the sole variable. Training students at five scales (0.5B to 14B) and evaluating on 18 benchmarks, we find that at matched FLOPs, IFT lies on or near the Pareto frontier across the majority of configurations. Reasoning reaches the Pareto frontier only on open-ended tasks at 7B and above. Even there, a sequential curriculum mixing just 25-50% reasoning data with IFT captures most of the accuracy benefit at far lower compute cost.

Nicolas Boizard, Hippolyte Gisserot-Boukhlef, Kevin El Haddad +2

1Diabolocom · 5MICS, CentraleSupélec, Université Paris-Saclay · 2Artefact Research Center +2

CoT Distillation LLM Fine-Tuning Efficient Language Model Reasoning Efficient Language Model Training Language Model Distillation Teacher-Student Learning

Aug 13, 2025cs.LG

Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

Xiaojun Wu, Xiaoguang Jiang, Huiyang Li +11

1Zhongxing Telecom Equipment(ZTE), China · 2China Mobile Communications Group Co Ltd

CoT Distillation Language Model Distillation Algorithmic Reasoning LLM Reasoning Data-Efficient Learning