Lightlike Neuromanifolds, Occam's Razor and Deep Learning
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Why do deep neural networks generalize with a very high dimensional parameter space? We took an information theoretic approach. We find that the dimensionality of the parameter space can be studied by singular semi-Riemannian geometry and is upper-bounded by the sample size. We adapt Fisher information to this singular neuromanifold. We use random matrix theory to derive a minimum description length of a deep learning model, where the spectrum of the Fisher information matrix plays a key role to improve generalisation.
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