Deep tensor networks with matrix product operators
This addresses efficiency challenges in neural networks for researchers in machine learning and tensor network theory, though it appears incremental as it builds on existing tensor network methods.
The paper tackles the problem of improving neural network efficiency by introducing deep tensor networks based on matrix product operators, achieving a 0.49% error rate on MNIST and 8.3% on FashionMNIST for image classification, and demonstrating exponential parameter reduction for sequence prediction compared to baseline methods.
We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalizes well to different input sizes.