Title: Contrastive Mutual Information Maximization for Binary Neural Networks. Abstract: Neural network binarization accelerates deep models by quantizing their weights and activations into 1-bit. However, there is still a huge performance gap between Binary Neural Networks (BNNs) and their full-precision counterparts. As the quantization error caused by weights binarization has been reduced in earlier works, the activations binarization becomes the major obstacle for further improvement of the accuracy. In spite of studies about the full-precision networks highlighting the distributions of activations, few works study the distribution of the binary activations in BNNs. In this paper, we introduce mutual information as the metric to measure the information shared by the binary and the latent full-precision activations. Then we maximize the mutual information by establishing a contrastive learning framework while training BNNs. Specifically, the representation ability of the BNNs is greatly strengthened via pulling the positive pairs with binary and full-precision activations from the same input samples, as well as pushing negative pairs from different samples (the number of negative pairs can be exponentially large). This benefits the downstream tasks, not only classification but also segmentation and depth estimation, etc. The experimental results show that our method can be implemented as a pile-up module on existing state-of-the-art binarization methods and can remarkably improve the performance over them on CIFAR-10/100 and ImageNet, in addition to the good generalization ability on NYUD-v2.