{"ID":2883970,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.08492","arxiv_id":"2508.08492","title":"Momentum Point-Perplexity Mechanics in Large Language Models","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.","short_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, ana...","url_abs":"https://arxiv.org/abs/2508.08492","url_pdf":"https://arxiv.org/pdf/2508.08492v1","authors":"[\"Lorenzo Tomaz\",\"Judd Rosenblatt\",\"Thomas Berry Jones\",\"Diogo Schwerz de Lucena\"]","published":"2025-08-11T21:50:34Z","proceeding":"cs.CL","tasks":"[\"cs.CL\",\"cs.AI\",\"cs.LG\"]","methods":"[\"Transformer\",\"Language Model\"]","has_code":false}