---
title: "Token Level Entropy Analysis"
created: 2026-04-06
updated: 2026-04-10
type: concept
tags: [distillation, optimization]
sources: []
---

# Token-Level Entropy Analysis

Token-level entropy analysis is a diagnostic technique for evaluating how well a student model preserves the uncertainty structure of a teacher model during knowledge distillation. It involves computing the Shannon entropy of the conditional output distribution at each token position and comparing histograms between teacher and student.

## Application in Distillation

In the context of [[entropy-aware-on-policy-distillation|EOPD]], this analysis revealed:

- Standard [[on-policy-distillation]] causes diversity collapse, retaining only 6.8% of high-entropy tokens (entropy >= 1.0) compared to 18.5% in the teacher.
- High-entropy tokens in reasoning tasks represent key decision points with multiple valid paths, not noise.
- EOPD preserves substantially more probability mass in the high-entropy region, staying closer to the teacher distribution.

## Methodology

1. Generate responses from teacher and student models on benchmark prompts.
2. For each token position t, compute H_t = -sum_x pi(x|c_t) * log pi(x|c_t).
3. Aggregate entropy values into histograms for comparison.

## Significance

This analysis provides direct evidence that mode-seeking objectives (reverse KL) fail to transfer distributional structure in uncertain regions, motivating entropy-aware training strategies.

[src: raw/ingested/2026/03/2603.07079.md]