Multiple Token Divergence: Measuring and Steering In-Context Computation Density

TL;DR

This paper introduces Multiple Token Divergence (MTD), a lightweight metric for measuring and controlling the computational effort of language models during in-context reasoning, correlating with task difficulty and accuracy.

Contribution

The paper proposes MTD as a novel, non-invasive measure of in-context computation effort and introduces Divergence Steering to control generated text complexity.

Findings

MTD effectively distinguishes complex from simple tasks

MTD correlates positively with problem difficulty on reasoning benchmarks

Lower MTD is associated with more accurate reasoning

Abstract

Measuring the in-context computational effort of language models is a key challenge, as metrics like next-token loss fail to capture reasoning complexity. Prior methods based on latent state compressibility can be invasive and unstable. We propose Multiple Token Divergence (MTD), a simple measure of computational effort defined as the KL divergence between a model's full output distribution and that of a shallow, auxiliary prediction head. MTD can be computed directly from pre-trained models with multiple prediction heads, requiring no additional training. Building on this, we introduce Divergence Steering, a novel decoding method to control the computational character of generated text. We empirically show that MTD is more effective than prior methods at distinguishing complex tasks from simple ones. On mathematical reasoning benchmarks, MTD correlates positively with problem difficulty. Lower MTD is associated with more accurate reasoning. MTD provides a practical, lightweight tool for analyzing and steering the computational dynamics of language models.