Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.30652

Recursive Self-Improvement via On-Policy Distillation for Reasoning

Shangjian Yin·Zehao Zhao·Kavosh Asadi·Rui Liu·Yuchen Lu·Shike Mei·Hang Cui·Luke Simon·Zhouxing Shi·Hamed Firooz
View original source ↗Read source document ↗Export metadata ↓

Abstract

On-policy distillation (OPD) trains a student model by having it generate trajectories, then matching its next-token predictions with an external teacher's next-token predictions. This provides dense, token-level supervision to the student. On-policy self-distillation (OPSD) eliminates the need for the external teacher. Specifically, a second frozen copy of the student model, now given the ground truth in its context, serves as the teacher. The student model only receives the problem and learns to mimic the privileged teacher model, while the teacher remains frozen throughout training. Previous work showed that freezing the teacher is useful for training stability, but we argue that this can prevent the teacher from incorporating the improvements learned by the student during training. Our primary contribution is to address this limitation with a recursive framework built around two complementary components. First, we let the privileged teacher co-evolve with the student so that revision learned in one round can guide the next, a process we refer to as Dynamic Co-Evolution (DCE). Second, because stronger revision can also make responses too verbose and self-critical, we additionally train on shorter, verified rewrites of the model's own on-policy responses. We call this complementary objective Self-Refined Concise Learning (SRCL). Overall, our comprehensive evaluations show that DCE+SRCL outperforms OPSD across multiple model scales and four competition-level mathematics benchmarks. Specifically, on Qwen3-8B, DCE+SRCL reaches 65.97% Average@12, outperforming OPSD by 35.62 percentage points while reducing mean output length by 7.80% relative to DCE alone.

Explore related subjects

cs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shangjian Yin, Zehao Zhao, Kavosh Asadi, Rui Liu, Yuchen Lu, Shike Mei, Hang Cui, Luke Simon, Zhouxing Shi, Hamed Firooz. 2026-09-25. Recursive Self-Improvement via On-Policy Distillation for Reasoning. https://arxiv.org/abs/2609.30652

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Boosting Large Language Models with Mask Fine-Tuning

The large language model (LLM) is typically integrated into the mainstream optimization protocol. However, it remains underexplored whether maintaining the model integrity is \textit{indispensable} for promising performance. In this work, we introduce Mask Fine-Tuning (MFT), a novel LLM fine-tuning paradigm demonstrating that carefully breaking the model's structural integrity can surprisingly improve performance without updating model weights. MFT learns and applies binary masks to well-optimized models, using the standard LLM fine-tuning objective as supervision. Based on fully fine-tuned models, MFT uses the same fine-tuning datasets to achieve consistent performance gains across domains and backbones (e.g., an average gain of 2.70/4.15 on IFEval with LLaMA2-7B/3.1-8B). Detailed ablation studies and analyses examine the proposed MFT from different perspectives, including the sparse ratio and the loss surface. Additionally, when deployed on well-trained models, MFT is compatible with other LLM optimization procedures to improve overall model performance. Furthermore, this study extends the masking operation beyond its conventional use in network pruning for model compression to encompass a broader range of model capabilities.

cs.CL↗
arXiv2026

Too Categorical to be Human: Emotion Concepts in LLMs and Humans

Understanding human emotions is central to user-facing AI applications, safety alignment, and the simulation of human behavior. As emotional stimuli shape high-stakes behavior in Large Language Models (LLMs), there is increasing interest in how models represent emotion concepts internally. Mechanistic accounts of these representations, however, cannot be compared directly against humans: emotion processing in humans is highly distributed and yields no equivalent neural representation. To understand whether LLMs internalize emotion concepts in a way similar to humans, we propose characterizing the abstract concept of an emotion using external behavioral signatures, which we term behavioral representations. Using the theory of cognitive appraisals, which enables representing emotional situations along interpretable evaluative dimensions, we create a benchmark dataset of emotional scenarios spanning 15 emotion categories. We elicit behavioral representations of emotion concepts from LLMs and humans using our benchmark, and study their structural similarity. We find that LLMs represent emotion concepts more categorically, homogeneously, and determinately than humans, representing a single emotion concept with less internal diversity, and place different emotions further apart. The categorical structure of representations in LLMs is further robust to contextual variation, including with different task framing and demographic personas. Analyzing model checkpoints across different training stages, we also find that the discretized nature of representations appears after the mid-training stage itself and is unaffected by different post-training strategies. Through our results, we highlight a key difference in how LLMs behaviorally represent emotion concepts, curbing the subjectivity inherent to the human experience of emotions.

cs.CL↗
arXiv2026

FedCoT: Communication-Efficient Federated Reasoning Enhancement for Large Language Models

Enhancing LLM reasoning in federated settings is nontrivial due to stringent computational, communication, and privacy constraints, especially in healthcare, where clinically consequential decisions require not only accuracy but also interpretable, auditable rationales to meet safety, accountability, and regulatory requirements. Conventional federated fine-tuning largely imitates final answers rather than cultivating step-by-step reasoning, often relying on privacy-sensitive centralized distillation and still incurring substantial communication overhead. We address this gap with \textbf{\ours{}}, a federated reasoning framework that combines lightweight chain-of-thought resampling with a compact discriminator for selection, and client-aware LoRA stacking with weighted classifier aggregation to accommodate heterogeneity while reducing aggregation noise and communication; clients generate candidate chains and supervision locally, and only lightweight modules are aggregated on the server. Experiments on medical reasoning benchmarks show consistent gains under tight resource budgets while keeping data local and respecting privacy, offering an interpretable and resource-efficient solution. Our code is made publicly available at https://github.com/DIaacKr/FedCoT

cs.CL↗