Cui, H. (2025). Architectural bias in a transport-based generative model : an asymptotic perspective. Perimeter Institute for Theoretical Physics. https://pirsa.org/25040092
MLA
Cui, Hugo. Architectural bias in a transport-based generative model : an asymptotic perspective. Perimeter Institute for Theoretical Physics, Apr. 10, 2025, https://pirsa.org/25040092
BibTex
@misc{ scivideos_PIRSA:25040092,
doi = {10.48660/25040092},
url = {https://pirsa.org/25040092},
author = {Cui, Hugo},
keywords = {},
language = {en},
title = {Architectural bias in a transport-based generative model : an asymptotic perspective},
publisher = {Perimeter Institute for Theoretical Physics},
year = {2025},
month = {apr},
note = {PIRSA:25040092 see, \url{https://scivideos.org/index.php/pirsa/25040092}}
}
We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of the resulting generated density, and evidence how mode(l) collapse can arise. On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.