Related papers: The Three-Legged Tree Tensor Networks with SU(2)- …
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
In this paper we propose a special type of a tree tensor network that has the geometry of a comb---a 1D backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of…
A three-family non-supersymmetric model with U(3)^3 gauge symmetry is analyzed in the context of intersecting D-branes. This is equivalent to the `trinification' model extended by three U(1) factors which survive as global symmetries in the…
We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…
Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…
How can we identify the training examples that contribute most to the prediction of a tree ensemble? In this paper, we introduce TREX, an explanation system that provides instance-attribution explanations for tree ensembles, such as random…
Classical shortest-path methods rely on binary tropical semirings $(\min,+)$, whose dyadic structure limits them to pairwise cost interactions. However, many real-world systems, including logistics, supply chains, communication networks,…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Single-affiliation systems are observed across nature and society. Examples include collaboration, organisational affiliations, and trade-blocs. The study of such systems is commonly approached through network analysis. Multilayer networks…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the…
We introduce efficient solutions to optimize the cost of tree-like tensor network state method calculations when an expensive GPU-accelerated hardware is utilized. By supporting a main powerful compute node with additional auxiliary, but…
Multilayer perceptrons (MLP), or fully connected artificial neural networks, are known for performing vector-matrix multiplications using learnable weight matrices; however, their practical application in many machine learning tasks,…