论文标题
量子张量网络机器学习的梯度下降方法的改进
Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning
论文作者
论文摘要
张量网络在无数不同的应用程序中表现出了机器学习的重要价值。但是，使用标准梯度下降优化张量网络已被证明在实践中很难。张量网络患有初始化问题，导致梯度爆炸或消失，并且需要大量的超参数调整。克服这些问题的努力通常取决于特定的网络体系结构或临时处方。在本文中，我们解决了初始化和高参数调整的问题，从而可以使用已建立的机器学习技术训练张量网络。我们引入了一种“复制节点”方法，该方法除了基于梯度的正规化技术以用于债券尺寸外，该方法成功初始化了任意张量网络。我们提出的数值结果表明，此处介绍的技术的组合产生了量子启发的张量网络模型，其参数要少得多，同时改善了概括性能。
Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks suffer from initialization problems resulting in exploding or vanishing gradients and require extensive hyperparameter tuning. Efforts to overcome these problems usually depend on specific network architectures, or ad hoc prescriptions. In this paper we address the problems of initialization and hyperparameter tuning, making it possible to train tensor networks using established machine learning techniques. We introduce a `copy node' method that successfully initializes arbitrary tensor networks, in addition to a gradient based regularization technique for bond dimensions. We present numerical results that show that the combination of techniques presented here produces quantum inspired tensor network models with far fewer parameters, while improving generalization performance.
