Title: Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification. Abstract: Modern deep neural networks (DNNs) require high memory consumption and large computational loads.  In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including the line of works on factorization methods. Factorization methods approximate the weight matrix of a DNN layer with multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter prevents DNN factorization from efficiently reaching a high compression rate. In this work, we propose SVD training, which first applies SVD to decompose DNN's layers and then performs training on the full-rank decomposed weights. To improve the training quality and convergence, we add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods. 