A library for optimization on Riemannian manifolds
A library for manifold-constrained optimization in TensorFlow.
To install the latest development version from GitHub:
pip install git+https://github.com/master/tensorflow-riemopt.git
To install a package from PyPI:
pip install tensorflow-riemopt
The core package implements concepts in differential geometry, such as manifolds and Riemannian metrics with associated exponential and logarithmic maps, geodesics, retractions, and transports. For manifolds, where closed-form expressions are not available, the library provides numerical approximations.
import tensorflow_riemopt as riemopt
S = riemopt.manifolds.Sphere()
x = S.projx(tf.constant([0.1, -0.1, 0.1]))
u = S.proju(x, tf.constant([1., 1., 1.]))
v = S.proju(x, tf.constant([-0.7, -1.4, 1.4]))
y = S.exp(x, v)
u_ = S.transp(x, y, u)
v_ = S.transp(x, y, v)
manifolds.Cholesky
- manifold of lower triangular matrices with positive diagonal elementsmanifolds.Euclidian
- unconstrained manifold with the Euclidean metricmanifolds.Grassmannian
- manifold of p
-dimensional linear subspaces of the n
-dimensional spacemanifolds.Hyperboloid
- manifold of n
-dimensional hyperbolic space embedded in the n+1
-dimensional Minkowski spacemanifolds.Poincare
- the Poincaré ball model of the hyperbolic spacemanifolds.Product
- Cartesian product of manifoldsmanifolds.SPDAffineInvariant
- manifold of symmetric positive definite (SPD) matrices endowed with the affine-invariant metricmanifolds.SPDLogCholesky
- SPD manifold with the Log-Cholesky metricmanifolds.SPDLogEuclidean
- SPD manifold with the Log-Euclidean metricmanifolds.SpecialOrthogonal
- manifold of rotation matricesmanifolds.Sphere
- manifold of unit-normalized pointsmanifolds.StiefelEuclidean
- manifold of orthonormal p
-frames in the n
-dimensional space endowed with the Euclidean metricmanifolds.StiefelCanonical
- Stiefel manifold with the canonical metricmanifolds.StiefelCayley
- Stiefel manifold the retraction map via an iterative Cayley transformConstrained optimization algorithms work as drop-in replacements for Keras optimizers for sparse and dense updates in both Eager and Graph modes.
optimizers.RiemannianSGD
- Riemannian Gradient Descentoptimizers.RiemannianAdam
- Riemannian Adam and AMSGradoptimizers.ConstrainedRMSProp
- Constrained RMSProplayers.ManifoldEmbedding
- constrained keras.layers.Embedding
layerIf you find TensorFlow RiemOpt useful in your research, please cite:
@misc{smirnov2021tensorflow,
title={TensorFlow RiemOpt: a library for optimization on Riemannian manifolds},
author={Oleg Smirnov},
year={2021},
eprint={2105.13921},
archivePrefix={arXiv},
primaryClass={cs.MS}
}
TensorFlow RiemOpt was inspired by many similar projects:
The code is MIT-licensed.