论文标题
带有矩阵产品运营商的深张量网络
Deep tensor networks with matrix product operators
论文作者
论文摘要
我们介绍了深张量网络，该网络是基于权重矩阵的张量网络表示的成倍宽神经网络。我们在图像分类（MNIST，FashionMnist）和序列预测（蜂窝自动机）任务上评估了提出的方法。在图像分类案例中，深度张量网络改善了我们的矩阵产品状态基线，并在MNIST上达到0.49％的错误率，而时尚士兵的错误率为8.3％。在序列预测情况下，我们证明了与一层张量网络方法相比，参数数量的指数改善。在这两种情况下，我们都讨论了非均匀和统一的张量网络模型，并表明后者可以很好地推广到不同的输入尺寸。
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.
