Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact marginal prior distributions of finite Bayesian neural networks   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.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio