README.rst

geoopt

Manifold aware pytorch.optim.

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

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.
• .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) – retraction map following vector u for time t
• .transp(u, t, v, *more) – transport vector v (and possibly more vectors) with direction u for time t
• .retr_transp(u, t, v, *more) – transport self, vector v (and possibly more vectors) with direction u for time t (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
• geoopt.Sphere - Sphere manifold ||x||=1

Optimizers

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

Samplers

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