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

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes Multiple Token Divergence (KL between a model's full next-token distribution and its shallow multi-token-prediction head) as a computational-effort measure, plus Divergence Steering, a geodesic-interpolation decoding method that biases generation toward or away from the MTP distribution.

Problem

Measuring in-context computational effort of language models, since next-token loss does not capture reasoning complexity, and prior latent-compressibility measures (PHi loss) are invasive and unstable to train.

Approach

Measure per-token computational effort as the KL divergence between the full model's output distribution and a shallow auxiliary MTP head's prediction, computable post hoc from existing MTP modules with no extra training; use the same geodesic (Fisher-Rao) interpolation between the two distributions as a decoding control knob alpha, complementary to temperature.

Key results

• MTD of MiMo-7B correlates positively with MATH difficulty (partial r=0.199 controlling for NLL on self-generated CoTs), while NLL correlates negatively (r=-0.158 uncontrolled).
• Selecting the lower-MTD CoT among correct/incorrect pairs yields 67.1% correct on MATH for MiMo, versus 73.3% for lower NLL and 80.4% when both agree.
• In creative writing, alpha=-0.1 gives the best Overall Impression score with MiMo; the optimum is negative with p<0.01 by quadratic regression.

Surprising findings

• Lower MTD is associated with correct reasoning, in contrast to prior PHi findings where correct answers had high PHi loss.
• MTD without access to the latest token embedding is negatively correlated with task complexity after controlling for NLL.

Limitations

• MTD may conflate genuine computation with simple patterns that exceed the shortcut head's capacity; results depend on MTP head size.
• Divergence steering gave no clear reasoning improvement for large pre-trained models in preliminary experiments.
• Correlations are modest (e.g., r around 0.2) and the Mistral results are quantitatively weaker than MiMo.

Experimental setup

Datasets: MATH GSM8K FineWeb

Benchmarks: MATH GSM8K creative writing benchmark

Metrics: partial correlation pairwise correct-CoT selection accuracy creativity score overall impression

Baselines: PHi loss next-token NLL

Builds on: Prediction of Hidden States (PHi) Multiple Token Prediction speculative decoding

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