An Empirical Analysis of the Advantages of Finite vs.~Infinite Width Bayesian Neural Networks

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 under model mis-specification, increasing width can hurt BNN performance. In these cases, we provide evidence that finite BNNs generalize better partially due to the properties of their frequency spectrum that allows them to adapt under model mismatch.