On some theoretical limitations of Generative Adversarial Networks

Benoît Oriol; Alexandre Miot

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arXiv · 2110.10915

On some theoretical limitations of Generative Adversarial Networks

Benoît Oriol·Alexandre Miot

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Abstract

Generative Adversarial Networks have become a core technique in Machine Learning to generate unknown distributions from data samples. They have been used in a wide range of context without paying much attention to the possible theoretical limitations of those models. Indeed, because of the universal approximation properties of Neural Networks, it is a general assumption that GANs can generate any probability distribution. Recently, people began to question this assumption and this article is in line with this thinking. We provide a new result based on Extreme Value Theory showing that GANs can't generate heavy tailed distributions. The full proof of this result is given.

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Benoît Oriol, Alexandre Miot. 2021-10-21. On some theoretical limitations of Generative Adversarial Networks. https://arxiv.org/abs/2110.10915

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