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• W2899686093 abstract "Though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they demonstrate many intriguing phenomena related to depth that are difficult to explain both theoretically and intuitively. Understanding how weights in deep networks coordinate together across layers to form useful learners has proven somewhat intractable, in part because of the repeated composition of nonlinearities induced by depth. We present a reparameterization of DNNs as a linear function of a particular feature map that is locally independent of the weights. This feature map transforms depth-dependencies into simple {em tensor} products and maps each input to a discrete subset of the feature space. Then, in analogy with logistic regression, we propose a max-margin assumption that enables us to present a so-called {em sample compression} representation of the neural network in terms of the discrete activation state of neurons induced by s vectors. We show how the number of support vectors relate to learning guarantees for neural networks through sample compression bounds, yielding a sample complexity O(ns/e) for networks with n neurons. Additionally, this number of support vectors has monotonic dependence on width, depth, and label noise for simple networks trained on the MNIST dataset." @default.
• W2899686093 created "2018-11-16" @default.
• W2899686093 creator A5000266658 @default.
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• W2899686093 date "2018-11-05" @default.
• W2899686093 modified "2023-09-24" @default.
• W2899686093 title "Generalization Bounds for Neural Networks: Kernels, Symmetry, and Sample Compression." @default.
• W2899686093 hasPublicationYear "2018" @default.
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