This website collects information from the tensor4all group which is working on tensor network methods based on tensor cross interpolation (TCI) and related tensor learning algorithms such as quantics/quantized tensor trains.
Literature
A pedagogical introduction to tensor network methods, which includes an overview of the existing literature and also new algorithms, can be found in:
Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, and Xavier Waintal, “Learning tensor networks with tensor cross interpolation: new algorithms and libraries”, arXiv:2407.02454.
Please check the reference page for more information on TCI and quantics tensor trains.
Code
We provide two software libraries that implement algorithms from the above manuscript for computing low-rank tensor representations. The code focuses on recent applications of tensor networks to objects that do not necessarily involve many-body quantum mechanics. It also contain known and new variants of the tensor cross interpolation (TCI) algorithm for unfolding tensors into tensor trains. One code is called Xfac (written in C++ with Python bindings), and a second implementation with similar functionality is based on Julia:
Monthly online meeting
We have a monthly online meeting to discuss the development of new methods and applications. Zoom links will be provided through a mailing list (49 registered users as of November 4th, 2024). Please contact us if you would like to join the mailing list.
Previous meetings:
- October 29th, 2024
- September 30th, 2024
- August 26th, 2024
- July 1st, 2024
- June 3rd, 2024
- April 22th, 2024
- March 25th, 2024
- February 22nd, 2024
Workshops
We organize workshops to discuss the development of new methods.
People
Check the about page to see who is involved in the tensor4all collaboration.
Frequently Asked Questions
We have a FAQ page to answer common questions.