PIRSA:25040092 Conference

DOI10.48660/25040092

Conference/School: Theory + AI Workshop: Theoretical Physics for AI

Cui, H. (2025). Architectural bias in a transport-based generative model : an asymptotic perspective. Perimeter Institute. https://pirsa.org/25040092

Cui, Hugo. Architectural bias in a transport-based generative model : an asymptotic perspective. Perimeter Institute, Apr. 10, 2025, https://pirsa.org/25040092 

@misc{ pirsa_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},
  year = {2025},
  month = {apr},
  note = {PIRSA:25040092 see, \url{https://pirsa.org}}
}

Abstract

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.

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