用于深度神经网络反演的提升Bregman公式
A Lifted Bregman Formulation for the Inversion of Deep Neural Networks
摘要：
我们提出了一个新的框架，用于深度神经网络的正则化反演。该框架是基于作者最近的工作训练前馈神经网络没有分化的激活函数。该框架通过引入辅助变量将参数空间提升到一个更高维的空间，并通过定制的Bregman距离惩罚这些变量。我们提出了一个家庭的变分regulationations这些Bregman距离的基础上，目前的理论结果和支持其实际应用的数值例子。特别是，我们提出了第一个收敛结果（据我们所知）的正则化反演的单层感知器，只假设逆问题的解决方案是在正则化算子的范围内，并表明正则化逆证明收敛到真正的逆，如果测量误差收敛到零。
英文摘要：
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.
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