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Robust Learning with Implicit Residual Networks...

by Viktor Reshniak, Clayton G Webster
Publication Type
Conference Paper
Journal Name
Machine Learning and Knowledge Extraction
Publication Date
Page Numbers
34 to 55
Conference Name
Thirty-third Conference on Neural Information Processing Systems
Conference Location
Vancouver, Canada
Conference Sponsor
Lambda, Lyft, Microsoft,, Citadel, Graphcore, Google AI, Saleforce Research, Apple, Amazon, Invenia Labs, Habana Labs, Voleon, QuantumBlack, NAVER corporation, Uber, Borealis AI, PDT Partners
Conference Date

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 for 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.