Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an alternative training scheme utilizing basic tensor network operations, e.g., summation and compression. The training algorithm is based on compressing the superposition state constructed from all the training data in product state representation. The algorithm could be parallelized easily and only iterates through the dataset once. Hence, it serves as a pre-training algorithm. We benchmark the algorithm on the MNIST dataset and show reasonable results for generating new images and classification tasks. Furthermore, we provide an interpretation of the algorithm as a compressed quantum kernel density estimation for the probability amplitude of input data.

翻译：张量网络近年来在监督学习和无监督学习的机器学习中得到了应用。训练这些模型最常用的方法是梯度下降法。在本工作中，我们考虑了一种利用基本张量网络操作（如求和与压缩）的替代训练方案。该训练算法基于对以乘积态表示的所有训练数据构建的叠加态进行压缩。该算法易于并行化，且仅需遍历数据集一次，因此可作为预训练算法使用。我们在MNIST数据集上对该算法进行了基准测试，展示了其在图像生成和分类任务中的合理表现。此外，我们将该算法解释为输入数据概率幅度的压缩量子核密度估计方法。