Depth induces scale-averaging in overparameterized linear Bayesian neural networks

• URL: http://arxiv.org/abs/2111.11954v1
• Date: Tue, 23 Nov 2021 15:48:47 GMT
• Title: Depth induces scale-averaging in overparameterized linear Bayesian neural networks
• Authors: Jacob A. Zavatone-Veth and Cengiz Pehlevan
• Abstract summary: Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels.
• Score: 20.864082353441685
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels. We leverage this observation to study representation learning in these networks, allowing us to connect limiting results obtained in previous studies within a unified framework. In total, these results advance our analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.

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