Algorithms developed to solve many-body quantum problems, like tensor
networks, can turn into powerful quantum-inspired tools to tackle problems in
the classical domain. In this work, we focus on matrix product operators, a
prominent numerical technique to study many-body quantum systems, especially in
one dimension. It has been previously shown that such a tool can be used for
classification, learning of deterministic sequence-to-sequence processes and of
generic quantum processes. We further develop a matrix product operator
algorithm to learn probabilistic sequence-to-sequence processes and apply this
algorithm to probabilistic cellular automata. This new approach can accurately
learn probabilistic cellular automata processes in different conditions, even
when the process is a probabilistic mixture of different chaotic rules. In
addition, we find that the ability to learn these dynamics is a function of the
bit-wise difference between the rules and whether one is much more likely than
the other.

利用矩阵乘积算子算法学习概率序列 - 序列过程，并将该算法应用于概率元胞自动机，可以准确学习不同条件下的概率元胞自动机过程，即使该过程是不同混沌规则的概率混合。

基于张量网络的概率元胞自动机动力学学习

Tensor-Networks-based Learning of Probabilistic Cellular Automata  Dynamics

The deep neural network (DNN) based speech enhancement approaches have
achieved promising performance. However, the number of parameters involved in
these methods is usually enormous for the real applications of speech
enhancement on the device with the limited resources. This seriously restricts
the applications. To deal with this issue, model compression techniques are
being widely studied. In this paper, we propose a model compression method
based on matrix product operators (MPO) to substantially reduce the number of
parameters in DNN models for speech enhancement. In this method, the weight
matrices in the linear transformations of neural network model are replaced by
the MPO decomposition format before training. In experiment, this process is
applied to the causal neural network models, such as the feedforward multilayer
perceptron (MLP) and long short-term memory (LSTM) models. Both MLP and LSTM
models with/without compression are then utilized to estimate the ideal ratio
mask for monaural speech enhancement. The experimental results show that our
proposed MPO-based method outperforms the widely-used pruning method for speech
enhancement under various compression rates, and further improvement can be
achieved with respect to low compression rates. Our proposal provides an
effective model compression method for speech enhancement, especially in
cloud-free application.

该论文提出了一种基于 MPO 的模型压缩方法，在神经网络模型的线性变换中将权重矩阵替换为 MPO 分解格式。实验结果表明，该方法在各种压缩率下均优于常用的修剪方法，特别适用于云端应用中的语音增强。

利用矩阵乘积算子的语音增强模型压缩方法

A Model Compression Method with Matrix Product Operators for Speech  Enhancement

A deep neural network is a parametrization of a multilayer mapping of signals
in terms of many alternatively arranged linear and nonlinear transformations.
The linear transformations, which are generally used in the fully connected as
well as convolutional layers, contain most of the variational parameters that
are trained and stored. Compressing a deep neural network to reduce its number
of variational parameters but not its prediction power is an important but
challenging problem toward the establishment of an optimized scheme in training
efficiently these parameters and in lowering the risk of overfitting. Here we
show that this problem can be effectively solved by representing linear
transformations with matrix product operators (MPOs), which is a tensor network
originally proposed in physics to characterize the short-range entanglement in
one-dimensional quantum states. We have tested this approach in five typical
neural networks, including FC2, LeNet-5, VGG, ResNet, and DenseNet on two
widely used data sets, namely, MNIST and CIFAR-10, and found that this MPO
representation indeed sets up a faithful and efficient mapping between input
and output signals, which can keep or even improve the prediction accuracy with
a dramatically reduced number of parameters. Our method greatly simplifies the
representations in deep learning, and opens a possible route toward
establishing a framework of modern neural networks which might be simpler and
cheaper, but more efficient.

本研究提出了使用矩阵积算子 (MPO) 来代替线性变换表示深度神经网络的方法，该方法可以最大限度地减少可变参数数量而不影响其预测能力，并在多个典型的神经网络上证明了其有效性和高效性。

通过矩阵乘积运算符对深度神经网络进行压缩

Compressing deep neural networks by matrix product operators

We show how to construct relevant families of matrix product operators in one
and higher dimensions. Those form the building blocks for the numerical
simulation methods based on matrix product states and projected entangled pair
states. In particular, we construct translational invariant matrix product
operators suitable for time evolution, and show how such descriptions are
possible for Hamiltonians with long-range interactions. We illustrate how those
tools can be exploited for constructing new algorithms for simulating quantum
spin systems.

本文介绍了如何构建矩阵乘积算符来进行量子系统的数值模拟，包括时间演化和长程相互作用下的 Hamiltonians，并给出了详细的应用示例。