# tensorflow-riemopt: A Library for Optimization on Riemannian Manifolds

arXiv: https://arxiv.org/abs/2105.13921 · HTML: https://mlsanity.com/paper/2105.13921/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [Building Deep Networks on Grassmann Manifolds](https://mlsanity.com/paper/1611.05742/) (2016)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [Optimization Techniques on Riemannian Manifolds](https://mlsanity.com/paper/1407.5965/) (2014)
- [Scalable Hyperbolic Recommender Systems](https://mlsanity.com/paper/1902.08648/) (2019)
- [McTorch, a manifold optimization library for deep learning](https://mlsanity.com/paper/1810.01811/) (2018)
- [Computing CNN Loss and Gradients for Pose Estimation with Riemannian Geometry](https://mlsanity.com/paper/1805.01026/) (2018)

## Built on by (most cited first, 5 of 5)

- [Riemannian Hamiltonian methods for min-max optimization on manifolds](https://mlsanity.com/paper/2204.11418/) (2022)
- [Differentially Private Fr'echet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metric](https://mlsanity.com/paper/2208.04245/) (2022)
- [Riemannian Optimization on Relaxed Indicator Matrix Manifold](https://mlsanity.com/paper/2503.20505/) (2025)
- [Rieoptax: Riemannian Optimization in JAX](https://mlsanity.com/paper/2210.04840/) (2022)
- [Tame Riemannian Stochastic Approximation](https://mlsanity.com/paper/2302.00709/) (2023)

## Abstract (arXiv)

This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on Riemannian manifolds, and stochastic optimization algorithms for non-Euclidean spaces. Designed for integration with TensorFlow Extended, it supports both research prototyping and production deployment of machine learning pipelines. The code and documentation are distributed under the MIT license and available at https://github.com/master/tensorflow-riemopt