# When Teachers Mislead: Spurious-Signal-Aware On-Policy Distillation

arXiv: https://arxiv.org/abs/2608.03632 · HTML: https://mlsanity.com/paper/2608.03632/

## 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 22 of its 27 references that are in the map.
- First posted on arXiv 4 Aug 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, 22 of 22)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Mitigating Hallucinations in Large Vision-Language Models with Instruction Contrastive Decoding](https://mlsanity.com/paper/2403.18715/) (2024)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Vision-OPD: Learning to See Fine Details for Multimodal LLMs via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.18740/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [MM-IFEngine: Towards Multimodal Instruction Following](https://mlsanity.com/paper/2504.07957/) (2025)
- [Video-OPD: Efficient Post-Training of Multimodal Large Language Models for Temporal Video Grounding via On-Policy Distillation](https://mlsanity.com/paper/2602.02994/) (2026)
- [Reinforcement-aware Knowledge Distillation for LLM Reasoning](https://mlsanity.com/paper/2602.22495/) (2026)
- [EvoChart: A Benchmark and a Self-Training Approach Towards Real-World Chart Understanding](https://mlsanity.com/paper/2409.01577/) (2024)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Shuffle-R1: Efficient RL framework for Multimodal Large Language Models via Data-centric Dynamic Shuffle](https://mlsanity.com/paper/2508.05612/) (2025)
- [Vero: An Open RL Recipe for General Visual Reasoning](https://mlsanity.com/paper/2604.04917/) (2026)

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

- [SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation](https://mlsanity.com/paper/2609.12579/) (2026)
- [VERPO: Verified Evidence Regularized Policy Optimization](https://mlsanity.com/paper/2609.06100/) (2026)
- [Unknown-Traffic Detection, Calibration and Shortcut Reliance in Distilled Encrypted-Traffic Classifiers over One Year](https://mlsanity.com/paper/2609.31141/) (2026)
- [OPSRD: On-Policy Self-Role Distillation](https://mlsanity.com/paper/2609.39884/) (2026)
- [DIAL-OPD: Learning More from Fewer Tokens in On-Policy Distillation](https://mlsanity.com/paper/2610.11659/) (2026)

## Abstract (arXiv)

On-Policy distillation (OPD) transfers teacher capabilities by supervising student-sampled trajectories with dense token-level teacher signals. Recent selective OPD methods improve this process by prioritizing signals that are confident, informative, or learnable. However, the assumptions overlook a fundamental failure mode of language models: their token-level judgments can be driven by input-agnostic language priors, formatting conventions, or stereotyped reasoning templates rather than task-specific evidence. We refer to such optimization-relevant but weakly input-grounded supervision as spurious signals in OPD, which may produce large gradients while contributing little task-improving direction. To mitigate this issue, we propose SA-OPD, a Spurious-Signal-Aware On-Policy Distillation framework that identifies and filters misleading token-level supervision based on input-groundedness and optimization impact. SA-OPD introduces a lightweight input-groundedness proxy estimating whether a token-level distillation signal truly depends on the input. It then filters only tokens that simultaneously exhibit low input-groundedness and extreme distillation divergence, thereby removing high-impact spurious updates and achieving fine-grained OPD optimization. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that SA-OPD consistently outperforms Vanilla OPD and competitive selective methods. These results establish input-groundedness as a key dimension for OPD supervision selection and offer a simple, effective strategy for mitigating spurious updates.