A lifted Bregman formulation for the inversion of deep neural networks

We propose a novel framework for the regularized inversion of deep neural networks. The is based on authors' recent work training feed-forward networks without differentiation activation functions. lifts parameter space into higher dimensional by introducing auxiliary variables, and penalizes these variables with tailored Bregman distances. family variational regularizations distances, present theoretical results support their practical application numerical examples. In particular, we first convergence result (to best our knowledge) single-layer perceptron that only assumes solution inverse problem in range regularization operator, shows provably converges to true if measurement errors converge zero.