# SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting

arXiv: https://arxiv.org/abs/2604.10688 · HTML: https://mlsanity.com/paper/2604.10688/

## Key facts

- Cited by 43 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 38 of its 40 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## 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 38)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (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)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (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)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)

## Built on by (most cited first, 30 of 43)

- [Asymmetric On-Policy Distillation: Bridging Exploitation and Imitation at the Token Level](https://mlsanity.com/paper/2605.06387/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Counteraction-Aware Multi-Teacher On-Policy Distillation for General Capability Recovery with Domain Preservation](https://mlsanity.com/paper/2605.27115/) (2026)
- [Rubric-based On-policy Distillation](https://mlsanity.com/paper/2605.07396/) (2026)
- [Look Ahead Before You Distill: Future Trajectory Validation of Teacher Guidance for Agentic On-Policy Distillation](https://mlsanity.com/paper/2608.01953/) (2026)
- [Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR](https://mlsanity.com/paper/2609.04108/) (2026)
- [Prefix-Guided On-Policy Distillation: Mining Golden Trajectories from Rollouts](https://mlsanity.com/paper/2606.21994/) (2026)
- [UniSD: Towards a Unified Self-Distillation Framework for Large Language Models](https://mlsanity.com/paper/2605.06597/) (2026)
- [ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation](https://mlsanity.com/paper/2606.23104/) (2026)
- [MAIGO: Mitigating Lost-in-Conversation with History-Cleaned On-Policy Self-Distillation](https://mlsanity.com/paper/2605.27186/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [Group-Reflective Self-Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.28076/) (2026)
- [Trust the Right Teacher: Quality-Aware Self-Distillation for GUI Grounding](https://mlsanity.com/paper/2606.18101/) (2026)
- [Behavior Cloning is Not All You Need: The Optimality of On-Policy Distillation for Noisy Expert Feedback](https://mlsanity.com/paper/2606.30923/) (2026)
- [Every Coin Has Two Sides: On the Dual Nature of Generalization in On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2608.16647/) (2026)
- [Beyond Teacher Likelihood: Group-Calibrated On-Policy Distillation for Long-Context Reasoning](https://mlsanity.com/paper/2608.19181/) (2026)
- [REOPD: Reliability-Adaptive Reward Extrapolation for On-Policy Distillation](https://mlsanity.com/paper/2608.11698/) (2026)
- [Beyond Imitation: Filtering On-Policy Distillation by Reasoning Progress](https://mlsanity.com/paper/2608.19408/) (2026)
- [Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation](https://mlsanity.com/paper/2609.16937/) (2026)
- [Restoring the Sweet Spot: Pass-Rate Weighted Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.27765/) (2026)
- [DAPD: Dual-Anchored Policy Distillation](https://mlsanity.com/paper/2608.01735/) (2026)
- [Learning from Consensus and Disagreement: Unsupervised On-Policy Self-Distillation with Minority-Trajectory Contrast](https://mlsanity.com/paper/2608.08764/) (2026)
- [Bidirectional Context Self-Distillation for Reinforcement Learning of Skill-Based LLM Agents](https://mlsanity.com/paper/2608.09555/) (2026)
- [DUET: Dual-Teacher On-Policy Distillation via Same-Weight Disagreement for Prohibition Compliance](https://mlsanity.com/paper/2608.14644/) (2026)
- [SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation](https://mlsanity.com/paper/2609.12579/) (2026)
- [From Parameters to Behaviors: A Survey of Model Fusion for Large Language Models](https://mlsanity.com/paper/2609.19553/) (2026)
- [Blockwise Policy-Drift Gating for On-Policy Distillation](https://mlsanity.com/paper/2606.24084/) (2026)
- [Not All Tokens Deserve Equal Credit: Counterfactual Sensitivity Credit Reallocation for Long-CoT Reasoning](https://mlsanity.com/paper/2607.27888/) (2026)
- [SMOPD: Selective Token-Entropy Masking for Dirty-History Multi-Turn On-Policy Self-Distillation](https://mlsanity.com/paper/2608.14647/) (2026)

## Abstract (arXiv)

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.