Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations

• URL: http://arxiv.org/abs/2102.06559v1
• Date: Fri, 12 Feb 2021 14:48:58 GMT
• Title: Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations
• Authors: Winnie Xu, Ricky T.Q. Chen, Xuechen Li, David Duvenaud
• Abstract summary: We perform scalable approximate inference in a recently-proposed family of continuous-depth neural networks. We demonstrate gradient-based variational inference, producing arbitrarily-flexible approximate posteriors. This approach further inherits the memory-efficient training and tunable precision of neural ODEs.
• Score: 37.02511585732081
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We perform scalable approximate inference in a recently-proposed family of continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer produces dynamics that follow a stochastic differential equation (SDE). 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 approaches the true posterior. This approach further inherits the memory-efficient training and tunable precision of neural ODEs.

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