A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits
Researchers have developed a theoretical framework to analyze Large Language Model (LLM) reasoning and out-of-distribution generalization using optimal transport. Their approach quantifies domain shifts with Wasserstein-1 distance and identifies two key limitations: position-dependent attention mechanisms hinder shift invariance, while sequential backtracking in Transformers imposes a circuit depth lower bound. Evaluations on combinatorial search tasks confirmed that generalization risk increases with domain shift, highlighting the necessity of physical layer depth scaling. AI
IMPACT Provides a theoretical framework for understanding LLM generalization, potentially guiding future architectural improvements.