# Weak-to-Strong Generalization via Direct On-Policy Distillation

arXiv: https://arxiv.org/abs/2607.05394 · HTML: https://mlsanity.com/paper/2607.05394/

## Key facts

- Cited by 18 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 14 of its 26 references that are in the map.
- First posted on arXiv 6 Jul 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, 14 of 14)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers](https://mlsanity.com/paper/1604.00825/) (2016)
- [Domain Adaptation via Minimax Entropy for Real/Bogus Classification of Astronomical Alerts](https://mlsanity.com/paper/2308.07538/) (2023)
- [Re-envisioning Euclid Galaxy Morphology: Identifying and Interpreting Features with Sparse Autoencoders](https://mlsanity.com/paper/2510.23749/) (2025)

## Built on by (most cited first, 18 of 18)

- [Visual Contrastive Self-Distillation](https://mlsanity.com/paper/2607.21556/) (2026)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling](https://mlsanity.com/paper/2608.11829/) (2026)
- [Simple-OPD: Demystifying Warm-up for On-policy Distillation](https://mlsanity.com/paper/2608.06802/) (2026)
- [Consolidating RLVR Capabilities Across Domains: A Deep Dive into Fusion Paradigms](https://mlsanity.com/paper/2608.27409/) (2026)
- [The Physics of Multi-Turn Long-Horizon Planning: From Pre-training to Post-training via Single- and Multi-Teacher On-Policy Agentic Distillation](https://mlsanity.com/paper/2607.24720/) (2026)
- [Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation](https://mlsanity.com/paper/2609.08798/) (2026)
- [Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition](https://mlsanity.com/paper/2609.14708/) (2026)
- [Not Every Token Is Worth Distilling: Selective Supervision for Direct-OPD](https://mlsanity.com/paper/2609.29142/) (2026)
- [MOPD-Router: Rethinking Teacher Routing in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2609.30837/) (2026)
- [Understanding the Synergy between SFT, RLVR, and OPD in LLM Post-Training](https://mlsanity.com/paper/2609.31900/) (2026)
- [Scaling Properties of Same-Family On-Policy Distillation](https://mlsanity.com/paper/2609.32722/) (2026)
- [Allspark: Weak to Strong Transfer via Alternating Chain of Thought](https://mlsanity.com/paper/2609.32913/) (2026)
- [Transfer-Stratified On-Policy Distillation for RL-Improved Reasoning Teachers](https://mlsanity.com/paper/2610.05974/) (2026)
- [On-Policy Distillation with Negative-Policy Rollouts](https://mlsanity.com/paper/2610.07874/) (2026)
- [Composing What Each Teacher Learned: Multi-Teacher On-Policy Distillation through Teacher-Relative Shifts](https://mlsanity.com/paper/2610.10460/) (2026)
- [DIAL-OPD: Learning More from Fewer Tokens in On-Policy Distillation](https://mlsanity.com/paper/2610.11659/) (2026)
- [Rethinking Relative Policy Differences Transfer of On-Policy Distillation](https://mlsanity.com/paper/2610.13205/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) is a powerful recipe for improving language-model reasoning, but it is expensive to repeat on every new strong model because the target model must generate many rollouts during training. As models scale, post-training itself becomes a bottleneck. We study a weak-to-strong alternative: run RL on a smaller model where rollouts are cheaper, then reuse what that RL run learned to improve a stronger target model. Directly distilling the post-RL weak teacher is not enough, because the teacher's final policy mixes useful RL gains with the limitations of the smaller model. We propose Direct On-Policy Distillation (Direct-OPD), which transfers the teacher's RL-induced policy shift instead. Direct-OPD compares the post-RL teacher with its own pre-RL reference and treats their log-ratio as a dense implicit reward for the student. In plain terms, the checkpoint pair tells us which actions RL made the weak model more or less likely to take, and Direct-OPD applies that signal on the stronger student's own on-policy states. This directly reuses the weak model's RL supervision signal without running sparse-reward RL on the target model. Empirically, Direct-OPD consistently leverages weaker teachers to improve stronger target models; notably, it boosts Qwen3-1.7B from 48.3% to 58.3% on AIME 2024 in just 4 hours on 8 A100 GPUs. It outperforms step-matched direct RL and enables the sequential composition of multiple policy shifts. Our results show that RL outcomes can be reused across model scales as implicit reward signals, not merely as final models to imitate.