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Conference Papers Year : 2022

On the expressivity of bi-Lipschitz normalizing flows

Abstract

An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Most state-of-the-art Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this paper, we discuss the expressivity of bi-Lipschitz Normalizing Flows and identify several target distributions that are difficult to approximate using such models. Then, we characterize the expressivity of bi-Lipschitz Normalizing Flows by giving several lower bounds on the Total Variation distance between these particularly unfavorable distributions and their best possible approximation. Finally, we discuss potential remedies which include using more complex latent distributions.
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Dates and versions

hal-03906979 , version 1 (19-12-2022)

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  • HAL Id : hal-03906979 , version 1

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Alexandre Vérine, Benjamin Negrevergne, Fabrice Rossi, Yann Chevaleyre. On the expressivity of bi-Lipschitz normalizing flows. ACML 2022 - 14th Asian Conference on Machine Learning,, Dec 2022, Hyderabad, India. ⟨hal-03906979⟩
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