# Can We Trust the Teacher? Decoupled Credit Direction-Magnitude for Self-Distillation

arXiv: https://arxiv.org/abs/2609.34848 · HTML: https://mlsanity.com/paper/2609.34848/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 28 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, 12 of 12)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [MMFineReason: Closing the Multimodal Reasoning Gap via Open Data-Centric Methods](https://mlsanity.com/paper/2601.21821/) (2026)
- [Reasoning emerges from constrained inference manifolds in large language models](https://mlsanity.com/paper/2605.08142/) (2026)

## Abstract (arXiv)

RLVR provides reliable trajectory-level credit, while OPSD offers dense supervision for token-level credit. This exposes a fundamental coupling when updating step-level credit direction and magnitude with teacher supervision, preventing steps from receiving reliable credit directions and contribution magnitudes, while making both vulnerable to teacher judgment errors and preference variance, as supported by our theoretical analysis. To separate credit direction from its contribution magnitude, we introduce textitDecoupled Credit Self-Distillation (DCSD), which theoretically decouples credit direction and magnitude into two reliable signals and uses them to calibrate privileged teacher supervision. Specifically, we design belief-margin probing to determine credit direction and marginal information gain to quantify credit magnitude, enabling step-to-token credit assignment for policy optimization. Across 11 benchmarks, DCSD achieves the best overall scores against GRPO, OPSD, RLSD, and RLCSD. Compared with base models, DCSD improves the overall score by 8.45 points on mathematical reasoning and 7.01 points on multimodal reasoning, while correcting the credit direction for 6% of tokens and yielding a 1.5× reduction in token credit magnitude.