Resources Worth Looking At

[MazenAli]

Great to see you guys undertake this project, would be nice to have a well maintained lib for these applications.

I am not sure if you are aware of some similar applications and libs, since you didn't mention them in your paper. But here are some refs that might be useful for you.

Anthony worked on some stuff regarding function approximation with adaptivity in both sparsity of cores and the tensor network structure: https://arxiv.org/abs/1912.07913
You can find more recent stuff here: https://anthony-nouy.github.io/publications.html

And he has a python lib implementing this, though I don't know how well maintained: https://anthony-nouy.github.io/tensap/

Might be helpful to consider some of the ideas or features for itensor NA.

[JoeyT1994]

Hi @MazenAli !

We are excited about the possibilities this library offers.

Thank you for making us aware of those references and that library, those will be helpful for us and could inspire us for certain features or ideas for ITensor NA.

[anthony-nouy]

Hi all,
I confirm that the library tensap is still maintained.
For related references on multivariate functions approximation using tree tensor networks, i suggest

• https://arxiv.org/abs/2007.01165 (theoretical results for supervised and unsupervised learning and model seelction strategy for ranks and trees). The minimax results for a large class of function classes are based on the following works with Mazen Ali. We have results for full or sparse cores.
  -https://arxiv.org/abs/1811.04455, https://arxiv.org/abs/1912.07913 (learning algorithms, possibly exploiting sparsity of cores)
• https://link.springer.com/article/10.1007/s00365-023-09620-w, https://arxiv.org/abs/2101.11932, https://arxiv.org/abs/2112.01474 (Approximation theory, analysis of approximation classes and convergence rates for a large class of smoothness classes)
• https://arxiv.org/abs/1705.00880, https://arxiv.org/abs/2104.13436 (active learning based on SCD/PCA)
  Best regards
• https://arxiv.org/abs/2310.08942 (some theoretical results on tensor formats with sparse cores)