Related papers: Permutation invariant tensor models and partition …

Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator,…

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…

Linear neural network layers that are either equivariant or invariant to permutations of their inputs form core building blocks of modern deep learning architectures. Examples include the layers of DeepSets, as well as linear layers…

Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…

In this paper we look at 3D lattice models that are generalizations of the state sum model used to define the Kuperberg invariant of 3-manifolds. The partition function is a scalar constructed as a tensor network where the building blocks…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…

Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under $S_N$, the symmetric group of all permutations of $N$ objects. In this paper, the permutation invariant…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…

Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…

Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…

In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

Multipartite quantum scenarios are a significant and challenging resource in quantum information science. Tensors provide a powerful framework for representing multipartite quantum systems. In this work, we introduce the role of…

The increasing use of multiple sensors, which produce a large amount of multi-dimensional data, requires efficient representation and classification methods. In this paper, we present a new method for multi-dimensional data classification…

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…

Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…