Francesco Tudisco

Associate Professor (Reader) in Machine Learning

School of Mathematics, The University of Edinburgh
The Maxwell Institute for Mathematical Sciences
School of Mathematics, Gran Sasso Science Institute JCMB, King’s Buildings, Edinburgh EH93FD UK
email: f dot tudisco at

Subhomogeneous Deep Equilibrium Models

Pietro Sittoni, Francesco Tudisco,
preprint, (2024)


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 assumptions on the parameter matrices, thus yielding a more flexible framework for well-defined implicit networks. We illustrate the performance of the resulting subhomogeneous networks on feed-forward, convolutional, and graph neural network examples.

Please cite this paper as:

  title = {Subhomogeneous Deep Equilibrium Models},
  author = {Pietro Sittoni and Tudisco, Francesco},
  journal = {arXiv:2403.00720},
  year = {2024}

Links: arxiv

Keywords: Deep learning neural networks perron-frobenius theory fixed points