Modern deep neural networks (DNNs) often 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 factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the 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 has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. 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 explicitly 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.

本研究提出了一种名为SVD training的神经网络压缩方法，通过正交性正则化和奇异值剪枝等技术，可以在训练过程中显式地实现降低矩阵秩的目标，从而更有效地减少DNN算法在低性能设备上的计算负担。

通过奇异向量正交正则化和奇异值稀疏化学习低秩深度神经网络