Robust learning with implicit residual networks

TL;DR

This paper introduces implicit residual networks inspired by implicit discretization schemes, enhancing stability, robustness, and generalization in deep learning architectures without adding parameters.

Contribution

It proposes a novel implicit residual block design, improving stability and robustness, and introduces a memory-efficient training algorithm and stochastic regularization.

Findings

Improved stability of forward and backward propagation.

Enhanced robustness and generalization capabilities.

Potential reduction in network depth due to stability improvements.

Abstract

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power and allows to control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet does not introduce new parameters and can potentially lead to a reduction in the number of required layers due to improved forward stability. Finally, we derive the memory-efficient training algorithm, propose a stochastic regularization technique and provide numerical results in support of our findings.