Riemannian Adaptive Optimization Methods with pytorch optim
Branch: master
Clone or download
ferrine logmap (#44)
* logmap

* set PR number in changelog
Latest commit 6b8f94a Feb 14, 2019
Type Name Latest commit message Commit time
Failed to load latest commit information.
docs A bit better public api (#40) Feb 12, 2019
geoopt logmap (#44) Feb 13, 2019
scripts Speed up geoopt (#15) Dec 9, 2018
tests logmap (#44) Feb 13, 2019
.gitignore Add Docs (#23) Jan 4, 2019
.travis.yml refactor code into torch.1.0.0 (#39) Feb 5, 2019
CHANGELOG.rst logmap (#44) Feb 13, 2019
LICENSE v0.0.1rc2 (#19) Dec 28, 2018
README.rst add expmaps (#43) Feb 13, 2019
requirements-dev.txt Add Docs (#23) Jan 4, 2019
setup.py refactor code into torch.1.0.0 (#39) Feb 5, 2019



Python Package Index Documentation Status Build Status Coverage Status Codestyle Black Gitter

Manifold aware pytorch.optim.

Unofficial implementation for “Riemannian Adaptive Optimization Methods” ICLR2019 and more.


Make sure you have pytorch>=1.0.0 installed

There are two ways to install geoopt:

  1. GitHub (preferred so far) due to active development
pip install git+https://github.com/ferrine/geoopt.git
  1. 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.


  • 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, t=1.) – retraction map following vector u for time t
  • .expmap(u, t=1.) – exponential map following vector u for time t (if expmap is not available in closed form, best approximation is used)
  • .transp(v, *more, u, t=1.) – transport vector v (and possibly more vectors) with direction u for time t
  • .retr_transp(v, *more, u, t=1.) – transport self, vector v (and possibly more vectors) with direction u for time t (returns are plain tensors)


  • 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
  • geoopt.Sphere - Sphere manifold ||x||=1

All manifolds implement methods necessary to manipulate tensors on manifolds and tangent vectors to be used in general purpose. See more in documentation.


  • geoopt.optim.RiemannianSGD – a subclass of torch.optim.SGD with the same API
  • geoopt.optim.RiemannianAdam – a subclass of torch.optim.Adam


  • geoopt.samplers.RSGLD – Riemannian Stochastic Gradient Langevin Dynamics
  • geoopt.samplers.RHMC – Riemannian Hamiltonian Monte-Carlo
  • geoopt.samplers.SGRHMC – Stochastic Gradient Riemannian Hamiltonian Monte-Carlo