论文标题
用于分类和回归的多尺度张量网络架构
A Multi-Scale Tensor Network Architecture for Classification and Regression
论文作者
论文摘要
我们提出了一种用于使用张量网络进行监督学习的算法，采用了通过一系列小波变换来进行粗粒的步骤，以进行预处理。我们将这些转换表示为一组张量网络层，与多尺度纠缠重新归一化ANSATZ（MERA）张量网络相同，并通过基于基于矩阵乘积状态（MPS）张量的模型执行监督的学习和回归任务，该模型在粗粒度数据上作用。由于整个模型由张量收缩组成（除了初始的非线性特征图外，我们还可以通过层向后的优化MPS模型自适应地细粒，而性能基本上没有损失。 MPS本身是使用基于密度基质重质化组（DMRG）算法的自适应算法训练的。我们通过在音频数据上执行分类任务和温度时间序列数据的回归任务来测试我们的方法，研究训练准确性对粗粒度层数的依赖性，并显示如何使用网络细分来初始化访问较好尺度特征的模型。
We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor network layers identical to those in a multi-scale entanglement renormalization ansatz (MERA) tensor network, and perform supervised learning and regression tasks through a model based on a matrix product state (MPS) tensor network acting on the coarse-grained data. Because the entire model consists of tensor contractions (apart from the initial non-linear feature map), we can adaptively fine-grain the optimized MPS model backwards through the layers with essentially no loss in performance. The MPS itself is trained using an adaptive algorithm based on the density matrix renormalization group (DMRG) algorithm. We test our methods by performing a classification task on audio data and a regression task on temperature time-series data, studying the dependence of training accuracy on the number of coarse-graining layers and showing how fine-graining through the network may be used to initialize models with access to finer-scale features.
