Geometric Analysis of Unconstrained Feature Models with $d=K$

Yi Shen; Shao Gu

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arXiv · 2407.10702

Geometric Analysis of Unconstrained Feature Models with $d=K$

Yi Shen·Shao Gu

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Abstract

Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the number of classes K. We demonstrate that two popular unconstrained feature models are strict saddle functions, with every critical point being either a global minimum or a strict saddle point that can be exited using negative curvatures. The primary findings conclusively confirm the conjecture on the unconstrained feature models in previous articles.

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Yi Shen, Shao Gu. 2024-07-15. Geometric Analysis of Unconstrained Feature Models with $d=K$. https://arxiv.org/abs/2407.10702

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