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Are Neurons Actually Collapsed? On the Fine-Grained Structure in Neural Representations
Yongyi Yang · Jacob Steinhardt · Wei Hu

Tue Jul 25 05:00 PM -- 06:30 PM (PDT) @ Exhibit Hall 1 #634

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.

Author Information

Yongyi Yang (University of Michigan - Ann Arbor)

Yongyi is a first-year Ph.D. student at University of Michigan, under the supervision of Prof. Wei Hu. His recent research interests include graph neural networks and the foundations of deep learning. Before that, Yongyi received Bachelor of Science from Fudan university, under the supervision of Prof. Xipeng Qiu. He also had an internship at Amazon Shanghai AI Lab and has his fortune to be advised by Dr. David Wipf and Prof. Zengfeng Huang.

Jacob Steinhardt (University of California, Berkeley)
Wei Hu (University of Michigan)

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