2023/06/29 by Yongyi Yang, Jacob Steinhardt, Yang, Yongyi +3 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Neural Network Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2306.17105
openalex publication_date 2023/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.