  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.
