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- W4324314938 abstract "The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both cross-entropy loss and mean square error can provably lead to NC. We remove NC's key assumption on the feature dimension and the number of classes, and then present a generalized neural collapse (GNC) hypothesis that effectively subsumes the original NC. Inspired by how NC characterizes the training target of neural networks, we decouple GNC into two objectives: minimal intra-class variability and maximal inter-class separability. We then use hyperspherical uniformity (which characterizes the degree of uniformity on the unit hypersphere) as a unified framework to quantify these two objectives. Finally, we propose a general objective -- hyperspherical uniformity gap (HUG), which is defined by the difference between inter-class and intra-class hyperspherical uniformity. HUG not only provably converges to GNC, but also decouples GNC into two separate objectives. Unlike cross-entropy loss that couples intra-class compactness and inter-class separability, HUG enjoys more flexibility and serves as a good alternative loss function. Empirical results show that HUG works well in terms of generalization and robustness." @default.
- W4324314938 created "2023-03-16" @default.
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- W4324314938 date "2023-03-11" @default.
- W4324314938 modified "2023-10-16" @default.
- W4324314938 title "Generalizing and Decoupling Neural Collapse via Hyperspherical Uniformity Gap" @default.
- W4324314938 doi "https://doi.org/10.48550/arxiv.2303.06484" @default.
- W4324314938 hasPublicationYear "2023" @default.
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