pypi (this might be significantly behind master branch)
pip install geoopt
The preferred way to install geoopt will change once stable project stage is achieved. Now, pypi is behind master as we actively develop and implement new features.
What is done so far
Work is in progress but you can already use this. Note that API might change in future releases.
Tensors
geoopt.ManifoldTensor – just as torch.Tensor with additional manifold keyword argument.
geoopt.ManifoldParameter – same as above, recognized in torch.nn.Module.parameters as correctly subclassed.
All above containers have special methods to work with them as with points on a certain manifold
.proj_() – inplace projection on the manifold.
.proju(u) – project vector u on the tangent space. You need to project all vectors for all methods below.
.egrad2rgrad(u) – project gradient u on Riemannian manifold
.inner(u, v=None) – inner product at this point for two tangent vectors at this point. The passed vectors are not projected, they are assumed to be already projected.
.retr(u) – retraction map following vector u
.expmap(u) – exponential map following vector u (if expmap is not available in closed form, best approximation is used)
.transp(v, u, *more) – transport vector v (and possibly more vectors) with direction u
.retr_transp(v, u, *more) – transport self, vector v (and possibly more vectors) with direction u (returns are plain tensors)
Manifolds
geoopt.Euclidean – unconstrained manifold in R with Euclidean metric
geoopt.Stiefel – Stiefel manifold on matrices A in R^{n x p} : A^t A=I, n >= p
All manifolds implement methods necessary to manipulate tensors on manifolds and tangent vectors to be used in general purpose. See more in documentation.
Optimizers
geoopt.optim.RiemannianSGD – a subclass of torch.optim.SGD with the same API
geoopt.optim.RiemannianAdam – a subclass of torch.optim.Adam
If you find this project useful in your research, please kindly add this bibtex entry in references.
@misc{geoopt,
author = {Max Kochurov and Sergey Kozlukov and Rasul Karimov and Viktor Yanush},
title = {Geoopt: Adaptive Riemannian optimization in PyTorch},
year = {2019},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {url{https://github.com/geoopt/geoopt}},
}