We investigate the benefit of treating all the parameters in a Bayesian
neural network stochastically and find compelling theoretical and empirical
evidence that this standard construction may be unnecessary. To this end, we
prove that expressive predictive distributions require only small amounts of
stochasticity. In particular, partially stochastic networks with only $n$
stochastic biases are universal probabilistic predictors for $n$-dimensional
predictive problems. In empirical investigations, we find no systematic benefit
of full stochasticity across four different inference modalities and eight
datasets; partially stochastic networks can match and sometimes even outperform
fully stochastic networks, despite their reduced memory costs.

本文研究采用贝叶斯神经网络随机化所有参数的好处，并发现在某种程度上，全随机结构可能是不必要的。我们证明表达能力强的预测分布只需要很少的随机性，部分随机网络只需具有 $n$ 个随机操作即可成为 $n$ 维预测问题的通用概率预测器。在经验调查中，我们发现在八个数据集中，部分随机网络比完全随机网络表现更好，且有时甚至可以匹敌或超越其性能，尽管它们的内存成本较低。