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

Tanush Kalhan, Anupam Chattopadhyay, Sriram Ranga, Amritendu Mukherjee

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. We then test whether density correlates with, and can be steered to improve, answer correctness. Experiments across six model scales, two training paradigms, and 60 GSM8K problems yield four main findings. First, lower LP variance predicts correctness in supervised fine-tuned (SFT) models, but this relationship weakens with scale and reverses in reinforcement-learning (RL) distilled models. Training paradigm therefore appears more influential than model size in determining density behaviour. 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…