Related papers: Tensor network simulations for nonorientable surfa…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…
Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
Building on recent work on capsule networks, we propose a new, general-purpose form of "routing by agreement" that activates output capsules in a layer as a function of their net benefit to use and net cost to ignore input capsules from…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…
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…
Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational…
Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…
Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification…
In this paper we present a computational model which decodes the spatio-temporal data from electro-physiological measurements of neuronal networks and reconstructs the network structure on a macroscopic domain, representing the connectivity…
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…