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Probabilistic neural networks are typically modeled with independent weightpriors, which do not capture weight correlations in the prior and do notprovide a parsimonious interface to express properties in function space. Adesirable class of priors would represent weights compactly, capturecorrelations between weights, facilitate calibrated reasoning aboutuncertainty, and allow inclusion of prior knowledge about the function spacesuch as periodicity or dependence on contexts such as inputs. To this end, thispaper introduces two innovations: (i) a Gaussian process-based hierarchicalmodel for network weights based on unit embeddings that can flexibly encodecorrelated weight structures, and (ii) input-dependent versions of these weightpriors that can provide convenient ways to regularize the function spacethrough the use of kernels defined on contextual inputs. We show these modelsprovide desirable test-time uncertainty estimates on out-of-distribution data,demonstrate cases of modeling inductive biases for neural networks with kernelswhich help both interpolation and extrapolation from training data, anddemonstrate competitive predictive performance on an active learning benchmark.

Hierarchical Gaussian Process Priors for Bayesian Neural Network Weights