A Lifted Bregman Formulation for the Inversion of Deep Neural Networks
This work addresses the challenge of inverting neural networks for applications like interpretability and data recovery, but it appears incremental as it builds on prior work without demonstrating broad practical impact.
The authors tackled the problem of regularized inversion of deep neural networks by proposing a lifted Bregman framework that introduces auxiliary variables and tailored Bregman distances, resulting in the first convergence proof for single-layer perceptron inversion under minimal assumptions.
We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors' recent work on training feed-forward neural networks without the differentiation of activation functions. The framework lifts the parameter space into a higher dimensional space by introducing auxiliary variables, and penalises these variables with tailored Bregman distances. We propose a family of variational regularisations based on these Bregman distances, present theoretical results and support their practical application with numerical examples. In particular, we present the first convergence result (to the best of our knowledge) for the regularised inversion of a single-layer perceptron that only assumes that the solution of the inverse problem is in the range of the regularisation operator, and that shows that the regularised inverse provably converges to the true inverse if measurement errors converge to zero.