# Learning What to Imitate: Entropy-Aware Distribution Mixing

arXiv: https://arxiv.org/abs/2610.06671 · HTML: https://mlsanity.com/paper/2610.06671/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 18 of 18)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [LeetCodeDataset: A Temporal Dataset for Robust Evaluation and Efficient Training of Code LLMs](https://mlsanity.com/paper/2504.14655/) (2025)
- [LFM2 Technical Report](https://mlsanity.com/paper/2511.23404/) (2025)
- [Entropy-Adaptive Fine-Tuning: Resolving Confident Conflicts to Mitigate Forgetting](https://mlsanity.com/paper/2601.02151/) (2026)
- [Towards On-Policy SFT: Distribution Discriminant Theory and its Applications in LLM Training](https://mlsanity.com/paper/2602.12222/) (2026)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [Entropy-Aware Token Rejection for Improving Speculative Decoding](https://mlsanity.com/paper/2512.23765/) (2025)
- [In Their Own Words: Reasoning Traces Tailored for Small Models Make Them Better Reasoners](https://mlsanity.com/paper/2509.22230/) (2025)

## Abstract (arXiv)

Small language models are often post-trained as students on reasoning traces from stronger teacher models to efficiently learn new skills. However, token-level imitation on traces that lie far outside the student's expected distribution often produces textitconfident conflicts, whereby the student is required to imitate a continuation that it deems unlikely (i.e., low-probability) despite being confident in a different continuation (i.e., in a low-entropy state). To mitigate the degradation in generalisation and catastrophic forgetting caused by these conflicts, we propose Entropy-Aware Mixing: a dynamic per-token interpolation of the student and teacher distributions, gated by the student's predictive entropy. We implement both convex and geometric interpolations for both offline trace generation (via speculative decoding, then SFT) and on-policy forward-KL distillation. Our results show that entropy-aware mixing stabilises distillation, improving in-distribution and out-of-distribution math reasoning while better preserving general capabilities than fixed-teacher supervision. Nonetheless, the optimal entropy schedule depends on the training source, with offline-generated traces favouring concave schedules (greater overall teacher influence) and on-policy training favouring linear or convex schedules (teacher concentrated in high-entropy states).