Disentangling Rich Dynamics from Feature Learning: A Framework for Independent Measurements (2410.04264v2)

Abstract: In machine learning, it is widely believed that dynamic feature transformation (the rich regime) enhances predictive performance. However, this link does not always hold, and existing richness measures rely on correlated factors - such as performance or parameter norms - which can complicate the analysis of feature learning. We introduce (1) a measure that quantifies the rich regime independently of performance, and (2) interpretable feature metrics for visualization. Leveraging low-rank bias, our approach generalizes neural collapse metrics and captures lazy-to-rich transitions (e.g., grokking) without relying on performance as a proxy. We reveal how batch normalization and training set size influence lazy/rich dynamics for VGG16 and ResNet18 on CIFAR-10/100, opening avenues for better understanding feature learning.