TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory

• URL: http://arxiv.org/abs/2508.10076v1
• Date: Wed, 13 Aug 2025 16:35:11 GMT
• Title: TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory
• Abstract summary: This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries.<n>We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries through the ``TensorMap'' type. We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries, illustrating its practical applications through select case studies.

Related papers

• PEPSKit.jl: A Julia package for projected entangled-pair state simulations [0.0]
  PEPSKit.jl is a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS)
  arXiv  Detail & Related papers  (2026-05-19T15:12:10Z)
• SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities [0.9556128246747769]
  SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings.<n>The key innovation supporting most of its functionality is a graph-theoretic tensor network canonicalizer.
  arXiv  Detail & Related papers  (2025-11-13T04:17:05Z)
• YASTN: Yet another symmetric tensor networks; A Python library for abelian symmetric tensor network calculations [0.0]
  We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array backend. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD, or simulating thermal states of the Hubbard model via imaginary time evolution.
  arXiv  Detail & Related papers  (2024-05-20T17:32:16Z)
• TensorKrowch: Smooth integration of tensor networks in machine learning [46.0920431279359]
  We introduceKrowch, an open source Python library built on top of PyTorch. Krowch allows users to construct any tensor network, train it, and integrate it as a layer in more intricate deep learning models.
  arXiv  Detail & Related papers  (2023-06-14T15:55:19Z)
• FAENet: Frame Averaging Equivariant GNN for Materials Modeling [123.19473575281357]
  We introduce a flexible framework relying on frameaveraging (SFA) to make any model E(3)-equivariant or invariant through data transformations. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling.
  arXiv  Detail & Related papers  (2023-04-28T21:48:31Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Equivariance with Learned Canonicalization Functions [77.32483958400282]
  We show that learning a small neural network to perform canonicalization is better than using predefineds. Our experiments show that learning the canonicalization function is competitive with existing techniques for learning equivariant functions across many tasks.
  arXiv  Detail & Related papers  (2022-11-11T21:58:15Z)
• When Random Tensors meet Random Matrices [50.568841545067144]
  This paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. We show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric textitblock-wise random matrix.
  arXiv  Detail & Related papers  (2021-12-23T04:05:01Z)
• Captum: A unified and generic model interpretability library for PyTorch [49.72749684393332]
  We introduce a novel, unified, open-source model interpretability library for PyTorch. The library contains generic implementations of a number of gradient and perturbation-based attribution algorithms. It can be used for both classification and non-classification models.
  arXiv  Detail & Related papers  (2020-09-16T18:57:57Z)
• Riemannian optimization of isometric tensor networks [0.0]
  We show how gradient-based optimization methods can be used to optimize tensor networks of isometries to represent e.g. ground states of 1D quantum Hamiltonians. We apply these methods in the context of infinite MPS and MERA, and show benchmark results in which they outperform the best previously-known optimization methods.
  arXiv  Detail & Related papers  (2020-07-07T17:19:05Z)
• Approximation with Tensor Networks. Part II: Approximation Rates for Smoothness Classes [0.0]
  We study the approximation by tensor networks (TNs) of functions from smoothness classes. The resulting tool can be interpreted as a feed-forward neural network. We show that arbitrary Besov functions can be approximated with optimal or near to optimal rate.
  arXiv  Detail & Related papers  (2020-06-30T21:57:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.