Related papers: Tensor network renormalization: application to dyn…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We…
Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the…
We propose a second renormalization group method to handle the tensor-network states or models. This method reduces dramatically the truncation error of the tensor renormalization group. It allows physical quantities of classical…
We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two…
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…
The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates…
Recurrent Neural Networks (RNNs) are widely used for modelling neural activity, yet the mathematical interplay of core procedures is used to analyze them (temporal rescaling, discretization, and linearization) remain uncharacterized. This…
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…
Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties…
The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…
Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
Network regularization is an effective tool for incorporating structural prior knowledge to learn coherent models over networks, and has yielded provably accurate estimates in applications ranging from spatial economics to neuroimaging…
Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS…
Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
We propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice…
Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…