EP245: The Geometric Shape of AI Reasoning

Title: A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation LimitsSource: http://arxiv.org/abs/2605.19944v1Summary:This paper establishes fundamental theoretical bounds for LLM reasoning, proving that scaling physical layer depth is a non-negotiable requirement for out-of-distribution generalization that cannot be bypassed by scaling width. It also formalizes why specific architectural choices, such as shift-invariant embeddings, are mathematically necessary to maintain reasoning equivariance across domain shifts.