🤖 AI Summary
Existing metrics—such as negative log-likelihood or latent state compressibility—fail to accurately quantify the implicit computational effort exerted by language models during contextual reasoning.
Method: We propose Multiple Token Divergence (MTD), a lightweight, training-free metric based on the KL divergence across multi-head prediction distributions. MTD quantifies implicit reasoning intensity via head-wise output divergence and enables Divergence Steering—a non-intrusive, plug-and-play decoding-time mechanism for adaptive inference depth control. Our approach integrates entropy-aware adaptive sampling with zero-shot evaluation.
Contribution/Results: MTD significantly outperforms compressibility-based baselines. In mathematical reasoning tasks, MTD values exhibit a strong positive correlation with problem difficulty and a robust negative correlation with answer accuracy, effectively stratifying inference load across reasoning-depth tiers.
📝 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.