Subhomogeneous Deep Equilibrium Models

arXiv:2403.00720v1 Announce Type: new
Abstract: Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years. However, these models often lack guarantees of existence and uniqueness, raising stability, performance, and reproducibility issues. In this paper, we present a new analysis of the existence and uniqueness of fixed points for implicit-depth neural networks based on the concept of subhomogeneous operators and the nonlinear Perron-Frobenius theory. Compared to previous similar analyses, our theory allows for weaker …

abstract analysis applications arxiv cs.lg cs.na equilibrium math.na math.oc networks neural networks paper performance reproducibility stability type