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# tntorch - Tensor Network Learning with PyTorch
**[Read the Docs site: *http://tntorch.readthedocs.io/*](http://tntorch.readthedocs.io/)**
[Welcome to *tntorch*](https://github.com/rballester/tntorch/blob/main/docs/tutorials/introduction.ipynb), a PyTorch-powered modeling and learning library using tensor networks. Such networks are unique in that [they use *multilinear* neural units](https://arxiv.org/abs/1711.00811) (instead of non-linear activation units). Features include:
- Basic and fancy **indexing** of tensors, **broadcasting**, **assignment**, etc.
- Tensor **decomposition** and **reconstruction**
- Element-wise and tensor-tensor **arithmetics**
- Building tensors from black-box functions using **cross-approximation**
- Finding global **maxima** and **minima** from tensors
- **Statistics** and **sensitivity analysis**
- **Optimization** using autodifferentiation
- **Misc. operations** on tensors: stacking, unfolding, sampling, derivating, etc.
- **Batch operations** (work in progress)
If you use this package, please cite our paper:
```
@article{UBS:22,
title = {tntorch: Tensor Network Learning with {P}y{T}orch},
journal = {Journal of Machine Learning Research},
volume = {forthcoming},
year = {2022},
author = {Mikhail Usvyatsov and Rafael Ballester-Ripoll and Konrad Schindler},
}
```
## Example Use Cases
Available [tensor formats](https://github.com/rballester/tntorch/blob/main/docs/tutorials/main_formats.ipynb) include:
- [CANDECOMP/PARAFAC (CP)](https://epubs.siam.org/doi/pdf/10.1137/07070111X)
- [Tucker](https://epubs.siam.org/doi/pdf/10.1137/S0895479898346995) (implemented as TT with increasing ranks, which has equal expressive power. Tucker factors are unconstrained matrices, unlike unitary/orthogonal matrices in some implementations.)
- [Tensor train (TT)](https://epubs.siam.org/doi/abs/10.1137/090752286?journalCode=sjoce3)
- Hybrids: CP-Tucker, TT-Tucker, etc.
- [Partial support](https://github.com/rballester/tntorch/blob/main/docs/tutorials/other_formats.ipynb) for other decompositions such as [INDSCAL, CANDELINC, DEDICOM, PARATUCK2](https://epubs.siam.org/doi/pdf/10.1137/07070111X), and custom formats
For example, the following networks both represent a 4D tensor (i.e. a real function that can take I1 x I2 x I3 x I4 possible values) in the TT and TT-Tucker formats:
In *tntorch*, **all tensor decompositions share the same interface**. You can handle them in a transparent form, as if they were plain NumPy arrays or PyTorch tensors:
```
> import tntorch as tn
> t = tn.randn(32, 32, 32, 32, ranks_tt=5) # Random 4D TT tensor of shape 32 x 32 x 32 x 32 and TT-rank 5
> print(t)
4D TT tensor:
32 32 32 32
| | | |
(0) (1) (2) (3)
/ \ / \ / \ / \
1 5 5 5 1
> print(tn.mean(t))
tensor(8.0388)
> print(tn.norm(t))
tensor(9632.3726)
```
Decompressing tensors is easy:
```
> print(t.torch().shape)
torch.Size([32, 32, 32, 32])
```
Thanks to PyTorch's automatic differentiation, you can easily define all sorts of loss functions on tensors:
```
def loss(t):
return torch.norm(t[:, 0, 10:, [3, 4]].torch()) # NumPy-like "fancy indexing" for arrays
```
Most importantly, loss functions can be defined on **compressed** tensors as well:
```
def loss(t):
return tn.norm(t[:3, :3, :3, :3] - t[-3:, -3:, -3:, -3:])
```
Check out the [introductory notebook](https://github.com/rballester/tntorch/blob/master/docs/tutorials/introduction.ipynb) for all the details on the basics.
## Tutorial Notebooks
- [Introduction](https://github.com/rballester/tntorch/blob/master/docs/tutorials/introduction.ipynb)
- [Active subspaces](https://github.com/rballester/tntorch/blob/master/docs/tutorials/active_subspaces.ipynb)
- [ANOVA decomposition](https://github.com/rballester/tntorch/blob/master/docs/tutorials/anova.ipynb)
- [Boolean logic](https://github.com/rballester/tntorch/blob/master/docs/tutorials/logic.ipynb)
- [Classification](https://github.com/rballester/tntorch/blob/master/docs/tutorials/classification.ipynb)
- [Cross-approximation](https://github.com/rballester/tntorch/blob/master/docs/tutorials/cross.ipynb)
- [Differentiable cross-approximation](https://github.com/rballester/tntorch/blob/master/docs/tutorials/diffcross.ipynb)
- [Differentiation](https://github.com/rballester/tntorch/blob/master/docs/tutorials/derivatives.ipynb)
- [Discrete/weighted finite automata](https://github.com/rballester/tntorch/blob/master/docs/tutorials/automata.ipynb)
- [Exponential machines](https://github.com/rballester/tntorch/blob/master/docs/tutorials/exponential_machines.ipynb)
- [Main tensor formats available](https://github.com/rballester/tntorch/blob/master/docs/tutorials/main_formats.ipynb)
- [Other custom formats](https://github.com/rballester/tntorch/blob/master/docs/tutorials/other_formats.ipynb)
- [Polynomial chaos expansions](https://github.com/rballester/tntorch/blob/master/docs/tutorials/pce.ipynb)
- [Tensor arithmetics](https://github.com/rballester/tntorch/blob/master/docs/tutorials/arithmetics.ipynb)
- [Tensor completion and regression](https://github.com/rballester/tntorch/blob/master/docs/tutorials/completion.ipynb)
- [Tensor decomposition](https://github.com/rballester/tntorch/blob/master/docs/tutorials/decompositions.ipynb)
- [Sensitivity analysis](https://github.com/rballester/tntorch/blob/master/docs/tutorials/sobol.ipynb)
- [Vector field data](https://github.com/rballester/tntorch/blob/master/docs/tutorials/vector_fields.ipynb)
## Installation
You can install *tntorch* using *pip*:
```
pip install tntorch
```
Alternatively, you can install from the source:
```
git clone https://github.com/rballester/tntorch.git
cd tntorch
pip install .
```
For functions that use cross-approximation, the optional package [*maxvolpy*](https://bitbucket.org/muxas/maxvolpy) is required (it can be installed via `pip install maxvolpy`).
## Testing
We use [*pytest*](https://docs.pytest.org/en/latest/). Simply run:
```
cd tests/
pytest
```
## Contributing
Pull requests are welcome!
Besides using the [issue tracker](https://github.com/rballester/tntorch/issues), feel also free to contact me at .