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Poster

Analysis of Learning a Flow-based Generative Model from Limited Sample Complexity

Hugo Cui · Florent Krzakala · Eric Vanden-Eijnden · Lenka Zdeborova

Halle B #75

Abstract: We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the means of the generated mixture and the mean of the target mixture, which we show decays as Θn(1n). Finally, this rate is shown to be in fact Bayes-optimal.

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