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• W3206494906 abstract "Bayesian neural networks are theoretically well-understood only in the infinite-width limit, where Gaussian priors over network weights yield Gaussian priors over network outputs. Recent work has suggested that finite Bayesian networks may outperform their infinite counterparts, but their non-Gaussian function space priors have been characterized only though perturbative approaches. Here, we derive exact solutions for the function space priors for individual input examples of a class of finite fully-connected feedforward Bayesian neural networks. For deep linear networks, the prior has a simple expression in terms of the Meijer $G$-function. The prior of a finite ReLU network is a mixture of the priors of linear networks of smaller widths, corresponding to different numbers of active units in each layer. Our results unify previous descriptions of finite network priors in terms of their tail decay and large-width behavior." @default.
• W3206494906 created "2021-10-25" @default.
• W3206494906 creator A5023195984 @default.
• W3206494906 creator A5063822685 @default.
• W3206494906 date "2021-04-23" @default.
• W3206494906 modified "2023-09-26" @default.
• W3206494906 title "Exact marginal prior distributions of finite Bayesian neural networks" @default.
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• W3206494906 hasPublicationYear "2021" @default.
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