Title: SnapQuant: A Probabilistic and Nested Parameterization for Binary Networks. Abstract: In this paper, we study the problem of training real binary weight networks (without layer-wise or filter-wise scaling factors) from scratch under the Bayesian deep learning perspective, meaning that the final objective is to approximate the posterior distribution of binary weights rather than reach a point estimation. The proposed method, named as SnapQuant, has two intriguing features: (1) The posterior distribution is parameterized as a policy network trained with a reinforcement learning scheme. During the training phase, we generate binary weights on-the-fly since what we actually maintain is the policy network, and all the binary weights are used in a burn-after-reading style. At the testing phase, we can sample binary weight instances for a given recognition architecture from the learnt policy network. (2) The policy network, which has a nested parameter structure consisting of layer-wise, filter-wise and kernel-wise parameter sharing designs, is applicable to any neural network architecture. Such a nested parameterization explicitly and hierarchically models the joint posterior distribution of binary weights. The performance of SnapQuant is evaluated with several visual recognition tasks including ImageNet. The code will be made publicly available.