Neural Network Expressive Power Analysis Via Manifold Topology
Primary Area: learning theory
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Keywords: neural network, topology, manifold
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Abstract: A prevalent assumption regarding real-world data is that it lies on or close to a lower-dimensional manifold. When deploying a neural network on data manifolds, the required size of the network heavily depends on the intricacy of the underlying latent manifold. While significant advancements have been made in understanding the geometric attributes of manifolds, it's essential to recognize that topology, too, is a fundamental characteristic of manifolds. In this study, we delve into a challenge where a classifier is trained with data on low-dimensional manifolds. We present an upper bound on the size of ReLU neural networks. This bound integrates the topological facets of manifolds, with empirical evidence confirming the tightness.
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Submission Number: 3904
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