Bayesian Neural Networks (BNNs) extend traditional neural networks to provide uncertainties associated with their outputs. On the forward pass through a BNN, predictions (and their uncertainties) are made either by Monte Carlo sampling network weights from the learned posterior or by analytically propagating statistical moments through the network. Though flexible, Monte Carlo sampling is computationally expensive and can be infeasible or impractical under resource constraints or for large networks. While moment propagation can ameliorate the computational costs of BNN inference, it can be difficult or impossible for networks with arbitrary nonlinearities, thereby restricting the possible set of network layers permitted with such a scheme. In this work, we demonstrate a simple yet effective approach for propagating statistical moments through arbitrary nonlinearities with only 3 deterministic samples, enabling few-sample variational inference of BNNs without restricting the set of network layers used. Furthermore, we leverage this approach to demonstrate a novel nonlinear activation function that we use to inject physics-informed prior information into output nodes of a BNN.

本研究通过仅使用3个确定性样本来传播统计矩，实现了对任意非线性网络层的统计矩传播，从而使得少样本变分推断成为可能，并将此方法应用于一种新的非线性激活函数，用于向Bayesian神经网络的输出节点注入物理先验信息。

任意非线性贝叶斯神经网络的小样本变分推断