Related papers: Interaction Decompositions for Tensor Network Regr…

Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most…

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…

Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…

Wireless-based activity sensing has gained significant attention due to its wide range of applications. We investigate radio-based multi-class classification of human activities using massive multiple-input multiple-output (MIMO) channel…

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…

Despite achieving state-of-the-art performance, deep learning methods generally require a large amount of labeled data during training and may suffer from overfitting when the sample size is small. To ensure good generalizability of deep…

In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the…

Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Transcriptomic data is a treasure-trove in modern molecular biology, as it offers a comprehensive viewpoint into the intricate nuances of gene expression dynamics underlying biological systems. This genetic information must be utilised to…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

Convolutional neural networks (CNNs) have gained widespread usage across various fields such as weather forecasting, computer vision, autonomous driving, and medical image analysis due to its exceptional ability to extract spatial…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of…

Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…