# Cornerstones or Stumbling Blocks? Deciphering the Rock Tokens in On-Policy Distillation

arXiv: https://arxiv.org/abs/2605.09253 · HTML: https://mlsanity.com/paper/2605.09253/

## Key facts

- Cited by 11 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 68 of its 87 references that are in the map.
- First posted on arXiv 10 May 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 68)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Large Language Models for Data Annotation and Synthesis: A Survey](https://mlsanity.com/paper/2402.13446/) (2024)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Preference Leakage: A Contamination Problem in LLM-as-a-judge](https://mlsanity.com/paper/2502.01534/) (2025)
- [Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models](https://mlsanity.com/paper/2402.19449/) (2024)
- [Can LLMs Learn from Previous Mistakes? Investigating LLMs' Errors to Boost for Reasoning](https://mlsanity.com/paper/2403.20046/) (2024)
- [Frequency-Aligned Knowledge Distillation for Lightweight Spatiotemporal Forecasting](https://mlsanity.com/paper/2507.02939/) (2025)
- [MAGMA: A Multi-Graph based Agentic Memory Architecture for AI Agents](https://mlsanity.com/paper/2601.03236/) (2026)
- [FineCIR: Explicit Parsing of Fine-Grained Modification Semantics for Composed Image Retrieval](https://mlsanity.com/paper/2503.21309/) (2025)
- [ReTrack: Evidence-Driven Dual-Stream Directional Anchor Calibration Network for Composed Video Retrieval](https://mlsanity.com/paper/2604.17898/) (2026)
- [Chat-Driven Text Generation and Interaction for Person Retrieval](https://mlsanity.com/paper/2509.12662/) (2025)
- [SepPrune: Structured Pruning for Efficient Deep Speech Separation](https://mlsanity.com/paper/2505.12079/) (2025)
- [DRP: Distilled Reasoning Pruning with Skill-aware Step Decomposition for Efficient Large Reasoning Models](https://mlsanity.com/paper/2505.13975/) (2025)
- [SGLP: A Similarity Guided Fast Layer Partition Pruning for Compressing Large Deep Models](https://mlsanity.com/paper/2410.14720/) (2024)
- [HABIT: Chrono-Synergia Robust Progressive Learning Framework for Composed Image Retrieval](https://mlsanity.com/paper/2604.18037/) (2026)
- [Delving Deeper: Hierarchical Visual Perception for Robust Video-Text Retrieval](https://mlsanity.com/paper/2601.12768/) (2026)

## Built on by (most cited first, 11 of 11)

- [When Safe Skills Collide: Measuring Compositional Risk in Agent Skill Ecosystems](https://mlsanity.com/paper/2606.00448/) (2026)
- [Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance](https://mlsanity.com/paper/2606.00305/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [CROP: Task Relevance via Counterfactuals for Selective On-Policy Distillation](https://mlsanity.com/paper/2608.13387/) (2026)
- [Right Knowledge, Wrong Answer: Characterizing Parametric Temporal Conflict in Open-Weight Language Models](https://mlsanity.com/paper/2606.20959/) (2026)
- [IMAGINE: Adaptive Schema-Imagery Enhanced Composition for Composed Video Retrieval](https://mlsanity.com/paper/2606.08144/) (2026)
- [OracleZoom: On-Policy Self-Distillation Inspired Reference-Constrained Recursive Image Super Resolution](https://mlsanity.com/paper/2609.06490/) (2026)
- [BEFORE THE FLIP: Measuring Hidden Score Shifts In Quantized Vision Language Models Before The Answer Changes for Visual Question Answering](https://mlsanity.com/paper/2609.06922/) (2026)
- [SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation](https://mlsanity.com/paper/2609.12579/) (2026)
- [A Shared Learning Rate Is Not a Neutral Control in Selective On-Policy Distillation](https://mlsanity.com/paper/2609.22109/) (2026)
- [Why On-Policy Distillation Sometimes Fails: Vanishing Learning Signals](https://mlsanity.com/paper/2610.11247/) (2026)

## Abstract (arXiv)

While recent work in Reinforcement Learning with Verifiable Rewards (RLVR) has shown that a small subset of critical tokens disproportionately drives reasoning gains, an analogous token-level understanding of On-Policy Distillation (OPD) remains largely unexplored. In this work, we investigate high-loss tokens, a token type that--as the most direct signal of student-teacher mismatch under OPD's per-token KL objective--should progressively diminish as training converges according to existing studies; however, our empirical analysis shows otherwise. Even after OPD training reaches apparent saturation, a substantial subset of tokens continues to exhibit persistently high loss; these tokens, which we term Rock Tokens, can account for up to 18% of the tokens in generated outputs. Our investigation reveals two startling paradoxes. First, despite their high occurrence frequency providing a disproportionately large share of total gradient norms, Rock Tokens themselves remain stagnant throughout training, resisting teacher-driven corrections. Second, through causal intervention, we find that these tokens provide negligible functional contribution to the model's actual reasoning performance. These findings suggest that a vast amount of optimization bandwidth is spent on structural and discourse residuals that the student model cannot or need not internalize. By deconstructing these dynamics, we demonstrate that strategically bypassing these ``stumbling blocks'' can significantly streamline the alignment process, challenging the necessity of uniform token weighting and offering a more efficient paradigm for large-scale model distillation.