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.
Connect with researchers working on tensor networks and related methods. Subscribe to our Google Groups mailing list for meeting announcements, join our Matrix space (chat) for real-time chat, or browse the Discourse archive.
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The Discourse forum is kept in read-only maintenance mode as an archive. Please use the mailing list for announcements and Matrix for live discussions.
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, Xavier Waintal, "Learning tensor networks with tensor cross interpolation: New algorithms and libraries", SciPost Phys. 18, 104 (2025) · published 20 March 2025, 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 (92 registered users as of January 5th, 2026). Please contact us if you would like to join the mailing list.
The Discourse forum is kept in read-only maintenance mode as an archive. Please use the mailing list for the latest announcements.
Planned meetings:
- May 26th, 2026 (Developer meeting: Christoph Groth, demonstration of his workflow using the pi harness for coding with AI agents, 8:00 AM EDT / 14:00 CEST / 21:00 JST; this meeting will be recorded)
Previous meetings:
- May 19th, 2026 (Developer meeting)
- May 12th, 2026 (talk: Paul Cazeaux, 8:00 AM EDT / 14:00 CEST / 21:00 JST)
- April 14th, 2026 (Developer meeting)
- March 17th, 2026 (Developer meeting)
- February 10th, 2026 (Developer meeting)
- January 20th, 2026 (talk: Prof. Engin Danis, "Tensor-Train Finite Difference Method for Compressible Flows", 8:00 AM ET / 14:00 CET / 22:00 JST) - Details
- July 8th, 2025 (talk: Leonhard Hoelscher)
- June 6th, 2025 (talk: Maksymilian Środa)
- May 6th, 2025
- March 1st, 2025
- February 18th, 2025
- January 13th, 2025 (talk: Yuehaw Khoo)
- 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.
We have a lectures page to share lectures on TCI and related tensor learning algorithms.
Check the about page to see who is involved in the tensor4all collaboration.
We have a FAQ page to answer common questions.