Momentum Point-Perplexity Mechanics in Large Language Models

• URL: http://arxiv.org/abs/2508.08492v1
• Date: Mon, 11 Aug 2025 21:50:34 GMT
• Title: Momentum Point-Perplexity Mechanics in Large Language Models
• Authors: Lorenzo Tomaz, Judd Rosenblatt, Thomas Berry Jones, Diogo Schwerz de Lucena,
• Abstract summary: We take a physics-based approach to studying how the internal hidden states of large language models change from token to token during inference.<n>We find that a quantity combining the rate of change in hidden states and the model's next-token certainty, analogous to energy in physics, remains nearly constant.<n>We derive a control method called Jacobian steering, which perturbs hidden states in the minimal way needed to favor a target token.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We take a physics-based approach to studying how the internal hidden states of large language models change from token to token during inference. Across 20 open-source transformer models (135M-3B parameters), we find that a quantity combining the rate of change in hidden states and the model's next-token certainty, analogous to energy in physics, remains nearly constant. Random-weight models conserve this "energy" more tightly than pre-trained ones, while training shifts models into a faster, more decisive regime with greater variability. Using this "log-Lagrangian" view, we derive a control method called Jacobian steering, which perturbs hidden states in the minimal way needed to favor a target token. This approach maintained near-constant energy in two tested models and produced continuations rated higher in semantic quality than the models' natural outputs. Viewing transformers through this mechanics lens offers a principled basis for interpretability, anomaly detection, and low-risk steering. This could help make powerful models more predictable and aligned with human intent.

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