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Title: Physical Mathematics for Deep Neural Networks
Abstract: Statistical Physics arose from the desire to understand the laws governing macroscopic bodies comprised of huge numbers of particles. By considering the average statistical properties of very large feedforward neural networks I will unveil the physical mechanism underlying Batch Normalization--a very successful optimization heuristic used in deep learning. I will also explain how symmetry considerations motivate a geometrical complexity notion that helps understand the generalization puzzle of deep learning; that is, why neural networks predict well on unseen test data despite having many more parameters than training examples.