Understanding Representation of Deep Equilibrium Models from Neural Collapse Perspective
Keywords: Deep Equilibrium Models, Neural Collapse, Imbalance learning
TL;DR: This paper analyzes the representation of DEQ from the Neural Collapse perspective under both balanced and imbalanced conditions.
Abstract: Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical analysis on the representation of DEQ. In this paper, we utilize the Neural Collapse ($\mathcal{NC}$) as a tool to systematically analyze the representation of DEQ under both balanced and imbalanced conditions. $\mathcal{NC}$ is an interesting phenomenon in the neural network training process that characterizes the geometry of class features and classifier weights. While extensively studied in traditional explicit neural networks, the $\mathcal{NC}$ phenomenon has not received substantial attention in the context of implicit neural networks.
We theoretically show that $\mathcal{NC}$ exists in DEQ under balanced conditions. Moreover, in imbalanced settings, despite the presence of minority collapse, DEQ demonstrated advantages over explicit neural networks. These advantages include the convergence of extracted features to the vertices of a simplex equiangular tight frame and self-duality properties under mild conditions, highlighting DEQ's superiority in handling imbalanced datasets. Finally, we validate our theoretical analyses through experiments in both balanced and imbalanced scenarios.
Primary Area: Deep learning architectures
Submission Number: 8805
Loading