AI RESEARCH
A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits
arXiv CS.AI
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ArXi:2605.19944v1 Announce Type: cross While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories into a continuous metric space to quantify domain shifts using the Wasserstein-1 distance. Invoking Kantorovich duality, we bound OOD generalization via architectural Lipschitz continuity and functional approximation limits. This exposes two primary constraints.