Related papers: Global Tensor Network Renormalization for 2D Quant…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…
We study the renormalization group flow of $\phi^4$ theory in two dimensions. Regularizing space into a fine-grained lattice and discretizing the scalar field in a controlled way, we rewrite the partition function of the theory as a tensor…
Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum…
We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate…
We propose a method of training quantization thresholds (TQT) for uniform symmetric quantizers using standard backpropagation and gradient descent. Contrary to prior work, we show that a careful analysis of the straight-through estimator…
In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…
Recovering the image of an object from its phaseless speckle pattern is difficult. Let alone the transmission matrix is unknown in multiple scattering media imaging. Double phase retrieval is a recently proposed efficient method which…
The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous…
Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…
The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
We present a tree-tensor-network-state (TTNS) method study of the ionic-neutral curve crossing of LiF. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, thus for quantum chemical…
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…
We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\hat\rho=e^{-\beta \hat{H}}$ onto itself. We refer to…
Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…