The Geometric Structure of Reasoning in Large Language Models

Large Language Models (LLMs) exhibit strong reasoning capabilities, yet the internal structure of these reasoning processes remains poorly understood. In this work, we show that reasoning in LLMs is implemented as geometric motion through structured manifolds in activation space. Using layer-wise trajectory analysis, we identify Punch Regions: recurrent high-curvature transition loci associated with reasoning-relevant state changes. We demonstrate that these regions are consistent across prompts, languages, and model architectures, and can be aligned into a shared coordinate frame, the B∗ Frame, which provides a basis for expressing and transferring conceptual dynamics. We further demonstrate that residual stream evolution through these geometric structures is governed by increasingly linear field dynamics, achieving near-perfect predictability (R²=~0.996) in the final layer. This progression reveals a phase transition from high dimensional semantic processing to low-dimensional output projection, answering the fundamental question of how abstract reasoning causally influences token selection. Punch Regions enable real-time detection of reasoning strategies prior to text generation, providing a mechanism for pre-action interpretability. Additionally, targeted interventions along Punch Region axes can steer the model’s reasoning trajectory, demonstrating conditional causal modulation of conceptual flow while preserving coherence. These findings characterize how reasoning is geometrically constrained, coordinated, and propagated in transformer architectures, providing a framework for understanding and influencing internal cognitive processes in large-scale neural models.The codebase is pending and greatly expands upon this work as well as proves utility.