Related papers: GrassmannTN: a Python package for Grassmann tensor…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
TensorBNN is a new package based on TensorFlow that implements Bayesian inference for modern neural network models. The posterior density of neural network model parameters is represented as a point cloud sampled using Hamiltonian Monte…
We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively…
A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-$1$) skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are…
Galaxy morphological classification is a fundamental aspect of galaxy formation and evolution studies. Various machine learning tools have been developed for automated pipeline analysis of large-scale surveys, enabling a fast search for…
We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors…
Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…
TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
We provide a new numerical procedure for constructing low coherence matrices, Trust-Region Stochastic Tuning for Matrix Incoherence (TRSTMI) and detail the results of experiments with a CPU/GPU parallelized implementation of this method.…
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
PESummary is a Python software package for processing and visualising data from any parameter estimation code. The easy to use Python executable scripts and extensive online documentation has resulted in PESummary becoming a key component…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
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…
This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on…
Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes…
GraphNeT is an open-source python framework aimed at providing high quality, user friendly, end-to-end functionality to perform reconstruction tasks at neutrino telescopes using graph neural networks (GNNs). GraphNeT makes it fast and easy…
We present a newly developed software package which implements a wide range of routines frequently used in Weak Gravitational Lensing (WL). With the continuously increasing size of the WL scientific community we feel that easy to use…