Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations

Abstract

We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive comparison against discrete-depth alternatives, while inheriting the memory-efficient training and tunable precision of Neural ODEs.

Cite

Text

Xu et al. "Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations." Artificial Intelligence and Statistics, 2022.

Markdown

[Xu et al. "Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations." Artificial Intelligence and Statistics, 2022.](https://mlanthology.org/aistats/2022/xu2022aistats-infinitely/)

BibTeX

@inproceedings{xu2022aistats-infinitely,
  title     = {{Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations}},
  author    = {Xu, Winnie and Chen, Ricky T. Q. and Li, Xuechen and Duvenaud, David},
  booktitle = {Artificial Intelligence and Statistics},
  year      = {2022},
  pages     = {721-738},
  volume    = {151},
  url       = {https://mlanthology.org/aistats/2022/xu2022aistats-infinitely/}
}