Are Neurons Actually Collapsed? On the Fine-Grained Structure in Neural Representations

TL;DR

This paper challenges the idea of Neural Collapse by showing that neural representations retain fine-grained structure that can be used to accurately reconstruct original labels, revealing more complexity than previously thought.

Contribution

The paper demonstrates that neural representations contain hidden fine-grained structure beyond Neural Collapse, enabling accurate label reconstruction and providing initial theoretical insights.

Findings

Representations can reconstruct original labels with 93% accuracy.

Fine-grained structure persists despite apparent collapse.

Theoretical results support the existence of detailed structure in simplified models.

Abstract

Recent work has observed an intriguing ''Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the last-layer representations are completely determined by the labels, and do not depend on the intrinsic structure of input distribution. We provide evidence that this is not a complete description, and that the apparent collapse hides important fine-grained structure in the representations. Specifically, even when representations apparently collapse, the small amount of remaining variation can still faithfully and accurately captures the intrinsic structure of input distribution. As an example, if we train on CIFAR-10 using only 5 coarse-grained labels (by combining two classes into one super-class) until convergence, we can reconstruct the original 10-class labels from the learned representations via unsupervised clustering. The reconstructed labels achieve $93\%$ accuracy on the CIFAR-10 test set, nearly matching the normal CIFAR-10 accuracy for the same architecture. We also provide an initial theoretical result showing the fine-grained representation structure in a simplified synthetic setting. Our results show concretely how the structure of input data can play a significant role in determining the fine-grained structure of neural representations, going beyond what Neural Collapse predicts.