# RISE: Recursive Improvement via Self-Extrapolating Policy Distillation

arXiv: https://arxiv.org/abs/2609.05295 · HTML: https://mlsanity.com/paper/2609.05295/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 65 of its 75 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

- 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 65)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (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)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)

## Built on by (most cited first, 5 of 5)

- [The Teacher Is a Direction, Not a Destination: Extrapolating RL-Induced Representation Residuals in On-Policy Distillation](https://mlsanity.com/paper/2609.36484/) (2026)
- [Teach Yourself Where to Look: On-Policy Attention Self-Distillation for Reasoning](https://mlsanity.com/paper/2609.33200/) (2026)
- [Train Ahead, Distill Back: Bootstrapping On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2609.37132/) (2026)
- [Collaborative Learning and Reasoning over Model Slices](https://mlsanity.com/paper/2610.12927/) (2026)
- [From Existing Methods to New Research Ideas: Two Perspectives on Recursive Self-Improvement](https://mlsanity.com/paper/2610.14625/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.