2021
DOI: 10.48550/arxiv.2101.09973
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Approximating Probability Distributions by ReLU Networks

Abstract: How many neurons are needed to approximate a target probability distribution using a neural network with a given input distribution and approximation error? This paper examines this question for the case when the input distribution is uniform, and the target distribution belongs to the class of histogram distributions. We obtain a new upper bound on the number of required neurons, which is strictly better than previously existing upper bounds. The key ingredient in this improvement is an efficient construction… Show more

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