The Density of Thought: Predicting and Steering Reasoning in Large Language Models

Key points

• We prompt frozen pretrained models to solve problems via CoT and measure the density of each reasoning step with two independent metrics: LP variance (how unevenly information is distributed across steps, computed as the variance in mean per-token negative log-likelihood) and the Caveman compression ratio.1
• We then test whether density correlates with, and can be steered to improve, answer correctness.1
• Second, synthetic experiments reveal an intrinsic complexity preference: models trained on uniformly distributed data learn complexity-favouring distributions 2.0 to 2.6 times more accurately than simplicity-favouring ones.1
• Finally, we introduce Entropy-Gated Density Routing (EGDR), a self-supervised method using token-level Shannon entropy to gate proportional KVcache adjustments during generation, improving accuracy by 10.0 percentage points without any external guidance.1

Sources (1)

• [1]The Density of Thought: Predicting and Steering Reasoning in Large Language Models
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 05:31 AM

  We investigate whether variation in information density across chain-of-thought (CoT) reasoning steps predicts answer correctness and can serve as a controllable inference-time target.

  We prompt frozen pretrained models to solve problems via CoT and measure the density of each reasoning step with two independent metrics: LP variance (how unevenly information is distributed across steps, computed as the variance in mean per-token negative log-likelihood) and the Caveman compression ratio.

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