Compact Model Training by Low-Rank Projection with Energy Transfer

Low-rankness plays an important role in traditional machine learning, but is not so popular in deep learning. Most previous low-rank network compression methods compress the networks by approximating pre-trained models and re-training. However, optimal solution in the Euclidean space may be quite different from the one in the low-rank manifold. A well pre-trained model is not a good initialization for the model with low-rank constraint. Thus, the performance of low-rank compressed network degrades significantly. Compared to other network compression methods such as pruning, low-rank methods attracts less attention in recent years. In this paper, we devise a new training method, low-rank projection with energy transfer (LRPET), that trains low-rank compressed networks from scratch and achieves competitive performance. First, we propose to alternately perform stochastic gradient descent training and projection onto the low-rank manifold. This asymptotically approaches the optimal solution in the low-rank manifold. Compared to re-training on compact model, this enables fully utilization of model capacity since solution space is relaxed back to Euclidean space after projection. Second, the matrix energy (the sum of squares of singular values) reduction caused by projection is compensated by energy transfer. We uniformly transfer the energy of the pruned singular values to the remaining ones. We theoretically show that energy transfer eases the trend of gradient vanishing caused by projection. Comprehensive experiment on CIFAR-10 and ImageNet have justified that our method is superior to other low-rank compression methods and also outperforms recent state-of-the-art pruning methods.