Multiple Token Divergence: Measuring and Steering In-Context Computation Density
This provides a practical tool for analyzing and steering computational dynamics in language models, addressing a key bottleneck in understanding model reasoning, though it is incremental as it builds on prior latent state methods.
The authors tackled the challenge of measuring in-context computational effort in language models by proposing Multiple Token Divergence (MTD), a simple metric based on KL divergence, and showed it effectively distinguishes complex tasks from simple ones, with lower MTD correlating with more accurate reasoning on mathematical benchmarks.
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.