GENERALIZATION, ROBUSTNESS AND ADAPTABILITY OF PROGRESSIVE NEURAL COLLAPSE

Jinxin Zhou, Jiachen Jiang, Zhihui Zhu

Keywords: Neural Collapse, generalization, robustness, domain adaptability

Abstract: Neural networks exhibit the neural collapse phenomenon in multi-class classification tasks, where last-layer features and linear classifier weights converge into a symmetric geometric structure. However, most prior studies have primarily focused on last-layer feature representations or have examined intermediate features using limited, simple architectures and datasets. The mechanisms by which deep neural networks separate data according to class membership across all layers in more complex and realistic scenarios, and how this separation evolves under distribution shifts, remain unclear. In this work, we extend the study of neural collapse to a broader range of architectures and datasets, investigating its progression throughout the network and its implications for generalization, robustness, and domain adaptability. Our findings reveal that well-trained neural networks progressively enhance neural collapse across layers, though a distinct transition phase occurs where this improvement plateaus after the initial layers and is followed by a renewed continuous improvement in the very last layers, with additional layers contributing minimal generalization benefits. Moreover, we observe that this progressive neural collapse pattern remains robust against noisy data, whether the noise occurs in inputs or labels, and that the degree of intermediate separation serves as an effective indicator of noise levels. Additionally, for the learned networks, comparing neural collapse evaluated on noisy data and clean data reveals insights into feature learning and memorization, with the latter primarily occurring in the very last layers. This finding aligns with the neural collapse pattern observed with clean training data. Finally, we show that when a shift occurs between source and target domains, intermediate neural collapse is closely related to downstream target performance.

Primary Area: interpretability and explainable AI

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Submission Number: 9044