Related papers: A Pairwise Connected Tensor Network Representation…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

In nuclear and particle physics one is often faced with problems where perturbation theory is not applicable. An example of this is the description of bound states. Therefore, an exact solution of field theory to all orders is an…

Dynamic networks have intrinsic structural, computational, and multidisciplinary advantages. Link prediction estimates the next relationship in dynamic networks. However, in the current link prediction approaches, only bipartite or…

Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…

Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where…

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…

We introduce an architecture, the Tensor Product Recurrent Network (TPRN). In our application of TPRN, internal representations learned by end-to-end optimization in a deep neural network performing a textual question-answering (QA) task…

Most state-of-the-art neural network potentials do not account for molecular attributes other than atomic numbers and positions, which limits its range of applicability by design. In this work, we demonstrate the importance of including…

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…

Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…

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…

Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…