Bayesian Neural Networks Avoid Encoding Complex and Perturbation-Sensitive Concepts

TL;DR

This paper investigates the concept encoding tendencies of Bayesian Neural Networks, showing they are less likely to encode complex and perturbation-sensitive concepts compared to standard neural networks, with theoretical proofs and experimental verification.

Contribution

It provides a theoretical analysis and experimental validation that Bayesian Neural Networks tend to encode simpler concepts, contrasting with standard deep neural networks.

Findings

BNNs are less likely to encode complex concepts

Experiments verify theoretical predictions

Complex concepts have low generalization and high vulnerability

Abstract

In this paper, we focus on mean-field variational Bayesian Neural Networks (BNNs) and explore the representation capacity of such BNNs by investigating which types of concepts are less likely to be encoded by the BNN. It has been observed and studied that a relatively small set of interactive concepts usually emerge in the knowledge representation of a sufficiently-trained neural network, and such concepts can faithfully explain the network output. Based on this, our study proves that compared to standard deep neural networks (DNNs), it is less likely for BNNs to encode complex concepts. Experiments verify our theoretical proofs. Note that the tendency to encode less complex concepts does not necessarily imply weak representation power, considering that complex concepts exhibit low generalization power and high adversarial vulnerability. The code is available at https://github.com/sjtu-xai-lab/BNN-concepts.