Constrained Deep Learning using Conditional Gradient and Applications in\n Computer Vision

A number of results have recently demonstrated the benefits of incorporating\nvarious constraints when training deep architectures in vision and machine\nlearning. The advantages range from guarantees for statistical generalization\nto better accuracy to compression. But support for general constraints within\nwidely used libraries remains scarce and their broader deployment within many\napplications that can benefit from them remains under-explored. Part of the\nreason is that Stochastic gradient descent (SGD), the workhorse for training\ndeep neural networks, does not natively deal with constraints with global scope\nvery well. In this paper, we revisit a classical first order scheme from\nnumerical optimization, Conditional Gradients (CG), that has, thus far had\nlimited applicability in training deep models. We show via rigorous analysis\nhow various constraints can be naturally handled by modifications of this\nalgorithm. We provide convergence guarantees and show a suite of immediate\nbenefits that are possible -- from training ResNets with fewer layers but\nbetter accuracy simply by substituting in our version of CG to faster training\nof GANs with 50% fewer epochs in image inpainting applications to provably\nbetter generalization guarantees using efficiently implementable forms of\nrecently proposed regularizers.\n