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We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…
We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety…
The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…
Neural Radiance Fields (NeRFs) are a very recent and very popular approach for the problems of novel view synthesis and 3D reconstruction. A popular scene representation used by NeRFs is to combine a uniform, voxel-based subdivision of the…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
We study the complexity of approximately contracting translation-invariant tensor networks. The computational cost of row-by-row tensor network contraction, which defines a discrete time evolution governed by a fixed transfer matrix, is…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
Vision Transformers have achieved state-of-the-art performance in a wide range of computer vision tasks, but their practical deployment is limited by high computational and memory costs. In this paper, we introduce a novel tensor-based…