# RLKD: Distilling LLMs' Reasoning via Reinforcement Learning

arXiv: https://arxiv.org/abs/2505.16142 · HTML: https://mlsanity.com/paper/2505.16142/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [Goal Misgeneralization in Deep Reinforcement Learning](https://mlsanity.com/paper/2105.14111/) (2021)
- [Search-in-the-Chain: Interactively Enhancing Large Language Models with Search for Knowledge-intensive Tasks](https://mlsanity.com/paper/2304.14732/) (2023)
- [SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction](https://mlsanity.com/paper/2410.09008/) (2024)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [Unsupervised Information Refinement Training of Large Language Models for Retrieval-Augmented Generation](https://mlsanity.com/paper/2402.18150/) (2024)
- [Everything is Editable: Extend Knowledge Editing to Unstructured Data in Large Language Models](https://mlsanity.com/paper/2405.15349/) (2024)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [Beyond Imitation: Learning Key Reasoning Steps from Dual Chain-of-Thoughts in Reasoning Distillation](https://mlsanity.com/paper/2405.19737/) (2024)

## Built on by (most cited first, 11 of 11)

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [LLM Latent Reasoning as Chain of Superposition](https://mlsanity.com/paper/2510.15522/) (2025)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Multi-Rollout On-Policy Distillation via Peer Successes and Failures](https://mlsanity.com/paper/2605.12652/) (2026)
- [Bridging Reasoning to Learning: Unmasking Illusions using Complexity Out of Distribution Generalization](https://mlsanity.com/paper/2510.06274/) (2025)
- [Structural Rationale Distillation via Reasoning Space Compression](https://mlsanity.com/paper/2605.07139/) (2026)
- [GateKD: Confidence-Gated Closed-Loop Distillation for Robust Reasoning](https://mlsanity.com/paper/2605.13136/) (2026)
- [ARKD: Adaptive Reinforcement Learning-Guided Bidirectional KL Divergence Distillation for Text Generation](https://mlsanity.com/paper/2606.29869/) (2026)
- [AdaStop: Cost-Aware Early Stopping for DNN Test Selection](https://mlsanity.com/paper/2607.05461/) (2026)
- [STAR-OPD: Structured Aspect-Cascade-Aware On-Policy Reward Distillation for ABSA Quadruple Extraction](https://mlsanity.com/paper/2608.20831/) (2026)
- [Look Before You Select: Rethinking Vocabulary Sparsification in On-Policy Distillation](https://mlsanity.com/paper/2609.34386/) (2026)

## Abstract (arXiv)

Distilling reasoning paths from teacher to student models via supervised fine-tuning (SFT) provides a shortcut for improving the reasoning ability of smaller Large Language Models (LLMs). However, the reasoning paths generated by teacher models often reflect only surface-level traces of their underlying authentic reasoning. Insights from cognitive neuroscience suggest that authentic reasoning involves a complex interweaving between meta-reasoning (which selects appropriate sub-problems from multiple candidates) and solving (which addresses the sub-problem). This implies authentic reasoning has an implicit multi-branch structure. Supervised fine-tuning collapses this rich structure into a flat sequence of token prediction in the teacher's reasoning path, preventing effective distillation of this structure to students. To address this limitation, we propose RLKD, a reinforcement learning (RL)-based distillation framework guided by a novel Generative Structure Reward Model (GSRM). Our GSRM converts reasoning paths into multiple meta-reasoning-solving steps and computes rewards to measure structural alignment between student and teacher reasoning. RLKD combines this reward with RL, enabling student LLMs to internalize the teacher's implicit multi-branch reasoning structure rather than merely mimicking fixed output paths. Experiments show RLKD surpasses standard SFT-RL pipelines even when trained on 0.1% of data under an RL-only regime, unlocking greater student reasoning potential than SFT-based distillation. Code is available at https://github.com/xsc1234/RLKD.