Qihan Ren

Qihan Ren, Huiqi Deng, Yunuo Chen et al.

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.

Qihan Ren, Jiayang Gao, Wen Shen et al.

This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.