Related papers: Notes on the Causal Structure in a Tensor Network
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Capsule networks are a neural network architecture specialized for visual scene recognition. Features and pose information are extracted from a scene and then dynamically routed through a hierarchy of vector-valued nodes called 'capsules'…
Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…
We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
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…
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
The problem of estimating high-dimensional network models arises naturally in the analysis of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks…
Accurate representation to an academic network is of great significance to academic relationship mining like predicting scientific impact. A Latent Factorization of Tensors (LFT) model is one of the most effective models for learning the…
The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…
Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is still a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
Bearing fault diagnosis is of great importance to decrease the damage risk of rotating machines and further improve economic profits. Recently, machine learning, represented by deep learning, has made great progress in bearing fault…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…