Geometric Analysis of Unconstrained Feature Models with $d=K$
This provides theoretical insights into training dynamics for researchers in deep learning, but it is incremental as it builds on prior work on Neural Collapse.
The paper tackles the problem of understanding Neural Collapse in deep neural networks by analyzing unconstrained feature models when the feature dimension equals the number of classes, demonstrating that critical points are either global minima or strict saddle points that can be exited using negative curvatures, confirming a previous conjecture.
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.