Riemannian optimization
38 papers with code • 0 benchmarks • 0 datasets
Optimization methods on Riemannian manifolds.
Benchmarks
These leaderboards are used to track progress in Riemannian optimization
Libraries
Use these libraries to find Riemannian optimization models and implementationsMost implemented papers
Riemannian Optimization for Skip-Gram Negative Sampling
Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent.
An Alternative to EM for Gaussian Mixture Models: Batch and Stochastic Riemannian Optimization
This motivates us to take a closer look at the problem geometry, and derive a better formulation that is much more amenable to Riemannian optimization.
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1.
Riemannian Optimization via Frank-Wolfe Methods
Both tasks involve geodesically convex interval constraints, for which we show that the Riemannian "linear" oracle required by RFW admits a closed-form solution; this result may be of independent interest.
Riemannian Adaptive Optimization Methods
Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings.
Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization
MIT-SPARK/FUSES
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We show that this approach, named Fast Unconstrained SEmidefinite Solver (FUSES), can solve large problems in milliseconds.
Spherical Text Embedding
While text embeddings are typically learned in the Euclidean space, directional similarity is often more effective in tasks such as word similarity and document clustering, which creates a gap between the training stage and usage stage of text embedding.
Geomstats: A Python Package for Riemannian Geometry in Machine Learning
geomstats/geomstats
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ICLR 2019
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more.
Operator-valued formulas for Riemannian Gradient and Hessian and families of tractable metrics
We provide an explicit formula for the Levi-Civita connection and Riemannian Hessian for a Riemannian manifold that is a quotient of a manifold embedded in an inner product space with a non-constant metric function.
Accurate and fast matrix factorization for low-rank learning
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices.
