An Empirical Analysis of the Advantages of Finite- v.s. Infinite-Width Bayesian Neural Networks

Abstract: Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we empirically compare finite- and infinite-width BNNs, and provide quantitative and qualitative explanations for their performance difference. We find that when the model is mis-specified, increasing width can hurt BNN performance. In these cases, we provide evidence that finite-width BNNs generalize better partially due to the properties of their frequency spectrum that allows them to adapt under model mismatch.