Description:

Neural Collapse in AI Training

X.Y. Han, Assistant Professor of Operations Management, Booth School of Business, University of Chicago

Abstract: In the performance-dominated landscape of AI development, systematic understanding is difficult: Any architecture is fair game as long as it can climb the leaderboard. Yet, even among the overwhelming multiformity of neural networks, one motif remains: data is transformed layer-by-layer and iteration-by-iteration into high-dimensional representations with which predictions are eventually made. Thus, examining the geometry of these representations offers a powerful lens for the analysis of AI. Neural Collapse is a striking example, evident late in the training of predictive AI: Originally observed in classification networks during a 'Terminal Phase of Training' (TPT) – where training error vanishes but loss continues decreasing – Neural Collapse reveals a fundamental inductive bias. It encompasses four interconnected geometric regularities in the final layer representations: (NC1) Within-class variability of activations collapses towards zero as they converge to their class means; (NC2) These class means arrange themselves into a maximally separated, symmetric structure (a Simplex Equiangular Tight Frame); (NC3) The classifier vectors align with these class means in a self-dual configuration; (NC4) The model's decision mechanism effectively simplifies to Nearest Class-Center rule. This emergent geometric simplicity is linked to improved generalization, robustness, and interpretability. I will discuss the core Neural Collapse phenomenon, its theoretical underpinnings, and recent updates and extensions since its discovery.