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.
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.
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:
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.
Planned meetings:
- January 13rd, 2025
Previous meetings:
- November 26th, 2024
- October 29th, 2024
- September 30th, 2024
- August 26th, 2024
- July 1st, 2024
- June 3rd, 2024
- April 22th, 2024
- March 25th, 2024
- February 22nd, 2024
We organize workshops to discuss the development of new methods.
Check the about page to see who is involved in the tensor4all collaboration.
We have a FAQ page to answer common questions.