There is growing evidence that the performance of a neural network depends largely on a small subset of its weights, which are typically identified by training a dense network and pruning it afterwards. Within a Bayesian framework, pruning can be directly incorporated through a spike-and-slab prior, providing a proper treatment of the uncertainties involved, both with respect to pruning and to parameter uncertainty. In Bayesian neural networks (BNNs), sampling by MCMC is notoriously hard. We demonstrate that modern Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) can be used to sample posteriors of BNNs asymptotically exact whenever numerically constructed rate bounds hold. Spike-and-slab priors can be incorporated through sticky versions of the PDMPs, setting weights exactly to zero during sampling. We examine the predictive performance and convergence of the samplers, and show that sparse BNNs sampled this way can be more robust to input noise than dense ones.

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