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Fractional Deep Neural Network via Constrained Optimization
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one another.
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization.
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