Provable Convergence of Tensor Decomposition-Based Neural Network Training

Advanced tensor decomposition, such as tensor train (TT), has been widely studied for tensor decomposition-based neural network (NN) training, which is one of the most common model compression methods. However, training NN with tensor decomposition always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for tensor decomposition-based NN training by formulating TT decomposition-based NN training as a nonconvex optimization problem. This problem can be solved by the proposed tensor block coordinate descent (tenBCD) method, which is a gradient-free algorithm. The global convergence of tenBCD to a critical point at a rate of O(1/k) is established with the Kurdyka {\L}ojasiewicz (K{\L}) property, where k is the number of iterations. The theoretical results can be extended to the popular residual neural networks (ResNets). The effectiveness and efficiency of our proposed framework are verified through an image classification dataset, where our proposed method can converge efficiently in training and prevent overfitting.