T3Toolbox#

A pure-Python (NumPy + optional JAX) library for Tucker tensor trains (T3). A Tucker tensor train is the composition of a Tucker decomposition with a tensor train decomposition of the central core. When the ranks are moderate, a T3 breaks the curse of dimensionality: storing a dense tensor costs O(N^d) memory, while the T3 representing it costs O(dnr^2 + dnN). Tucker tensor trains are also known as extended tensor trains (ETT).

The library provides the T3 format itself (arithmetic, orthogonalization, T3-SVD), the three sampling operations (entries / apply / probe) and their derivatives, the fixed-rank T3 manifold with tangent vectors and Riemannian geometry, least-squares fitting with four optimizers (residual weighting, regularization and rank continuation included), optimization over shared Tucker factors (SF-T3), diagonal edge weighting of tensors and tangent coordinates, and a mask-based uniform (padded, GPU/jit-friendly) mirror of the whole stack.

Installation#

The package is pure Python. Dependencies:

pip install t3toolbox

To include the optional JAX backend:

pip install "t3toolbox[jax]"

From source (development install):

git clone https://github.com/NickAlger/T3Toolbox.git
cd T3Toolbox
pip install -e .

Websites#

Authors#

MIT License. To cite T3Toolbox, cite the software itself (the repository’s CITATION.cff). The library grew out of the research in Alger, Christierson, Chen & Ghattas (2026), “Tucker Tensor Train Taylor Series” (arXiv:2603.21141), where many of the core algorithms are described — cite that paper when you build on its research contributions; see Relevant literature for the wider background.

Indices#