Defining Neural Network Architecture through Polytope Structures of Dataset

Current theoretical and empirical research in neural networks suggests that complex datasets require large network architectures for thorough classification, yet the precise nature of this relationship remains unclear. This paper tackles this issue by defining upper and lower bounds for neural network widths, which are informed by the polytope structure of the dataset in question. We also delve into the application of these principles to simplicial complexes and specific manifold shapes, explaining how the requirement for network width varies in …

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