Related papers: Containments of Tensor Network Varieties
We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) 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…
Tree tensor networks such as the tensor train format are a common tool for high dimensional problems. The associated multivariate rank and accordant tuples of singular values are based on different matricizations of the same tensor. While…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
In this article we study a special class of vector bundles, called tensors. A tensor consists of a vector bundle $E$ over a smooth irreducible projective variety and a morphism of vector bundles $\varphi$. As for classical vector bundles,…
Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
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…
An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
We define three types of upper (and lower) triangular blocked tensors, which are all generalizations of the triangular blocked matrices. We study some basic properties and characterizations of these three types of triangular blocked…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy--a rooted, binary, timed tree, with tips corresponding…
A capsule is a collection of neurons which represents different variants of a pattern in the network. The routing scheme ensures only certain capsules which resemble lower counterparts in the higher layer should be activated. However, the…
We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…
"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but…
The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…