Robust learning with implicit residual networks
This work addresses robustness and efficiency issues in deep learning for researchers and practitioners, though it appears incremental as it builds on existing ResNet architectures.
The authors tackled the problem of improving stability and generalization in deep neural networks by proposing implicit residual blocks defined as fixed points of nonlinear transformations, resulting in enhanced forward and backward propagation stability and potential reduction in required layers without new parameters.
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.