A library for optimization on Riemannian manifolds

Overview

TensorFlow RiemOpt

PyPI arXiv Build Status Coverage Status Code style: black License

A library for manifold-constrained optimization in TensorFlow.

Installation

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

Features

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

  • manifolds.Cholesky - manifold of lower triangular matrices with positive diagonal elements
  • manifolds.Euclidian - unconstrained manifold with the Euclidean metric
  • manifolds.Grassmannian - manifold of p-dimensional linear subspaces of the n-dimensional space
  • manifolds.Hyperboloid - manifold of n-dimensional hyperbolic space embedded in the n+1-dimensional Minkowski space
  • manifolds.Poincare - the Poincaré ball model of the hyperbolic space
  • manifolds.Product - Cartesian product of manifolds
  • manifolds.SPDAffineInvariant - manifold of symmetric positive definite (SPD) matrices endowed with the affine-invariant metric
  • manifolds.SPDLogCholesky - SPD manifold with the Log-Cholesky metric
  • manifolds.SPDLogEuclidean - SPD manifold with the Log-Euclidean metric
  • manifolds.SpecialOrthogonal - manifold of rotation matrices
  • manifolds.Sphere - manifold of unit-normalized points
  • manifolds.StiefelEuclidean - manifold of orthonormal p-frames in the n-dimensional space endowed with the Euclidean metric
  • manifolds.StiefelCanonical - Stiefel manifold with the canonical metric
  • manifolds.StiefelCayley - Stiefel manifold the retraction map via an iterative Cayley transform

Optimizers

Constrained 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 Descent
  • optimizers.RiemannianAdam - Riemannian Adam and AMSGrad
  • optimizers.ConstrainedRMSProp - Constrained RMSProp

Layers

  • layers.ManifoldEmbedding - constrained keras.layers.Embedding layer

Examples

  • SPDNet - Huang, Zhiwu, and Luc Van Gool. "A Riemannian network for SPD matrix learning." Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence. AAAI Press, 2017.
  • LieNet - Huang, Zhiwu, et al. "Deep learning on Lie groups for skeleton-based action recognition." Proceedings of the IEEE conference on computer vision and pattern recognition. 2017.
  • GrNet - Huang, Zhiwu, Jiqing Wu, and Luc Van Gool. "Building Deep Networks on Grassmann Manifolds." AAAI. AAAI Press, 2018.
  • Hyperbolic Neural Network - Ganea, Octavian, Gary Bécigneul, and Thomas Hofmann. "Hyperbolic neural networks." Advances in neural information processing systems. 2018.
  • Poincaré GloVe - Tifrea, Alexandru, Gary Becigneul, and Octavian-Eugen Ganea. "Poincaré Glove: Hyperbolic Word Embeddings." International Conference on Learning Representations. 2018.

References

If 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}
}

Acknowledgment

TensorFlow RiemOpt was inspired by many similar projects:

  • Manopt, a matlab toolbox for optimization on manifolds
  • Pymanopt, a Python toolbox for optimization on manifolds
  • Geoopt: Riemannian Optimization in PyTorch
  • Geomstats, an open-source Python package for computations and statistics on nonlinear manifolds

License

The code is MIT-licensed.

You might also like...
Distributed Asynchronous Hyperparameter Optimization better than HyperOpt.
Distributed Asynchronous Hyperparameter Optimization better than HyperOpt.

UltraOpt : Distributed Asynchronous Hyperparameter Optimization better than HyperOpt. UltraOpt is a simple and efficient library to minimize expensive

Official code for paper "Optimization for Oriented Object Detection via Representation Invariance Loss".

Optimization for Oriented Object Detection via Representation Invariance Loss By Qi Ming, Zhiqiang Zhou, Lingjuan Miao, Xue Yang, and Yunpeng Dong. Th

Keras + Hyperopt: A very simple wrapper for convenient hyperparameter optimization

This project is now archived. It's been fun working on it, but it's time for me to move on. Thank you for all the support and feedback over the last c

Bayesian optimization in PyTorch

BoTorch is a library for Bayesian Optimization built on PyTorch. BoTorch is currently in beta and under active development! Why BoTorch ? BoTorch Prov

optimization routines for hyperparameter tuning
optimization routines for hyperparameter tuning

Optunity is a library containing various optimizers for hyperparameter tuning. Hyperparameter tuning is a recurrent problem in many machine learning t

Distributed Asynchronous Hyperparameter Optimization in Python

Hyperopt: Distributed Hyperparameter Optimization Hyperopt is a Python library for serial and parallel optimization over awkward search spaces, which

Hyper-parameter optimization for sklearn

hyperopt-sklearn Hyperopt-sklearn is Hyperopt-based model selection among machine learning algorithms in scikit-learn. See how to use hyperopt-sklearn

A Python implementation of global optimization with gaussian processes.
A Python implementation of global optimization with gaussian processes.

Bayesian Optimization Pure Python implementation of bayesian global optimization with gaussian processes. PyPI (pip): $ pip install bayesian-optimizat

Safe Bayesian Optimization
Safe Bayesian Optimization

SafeOpt - Safe Bayesian Optimization This code implements an adapted version of the safe, Bayesian optimization algorithm, SafeOpt [1], [2]. It also p

Comments
  • Projection on SPDs is not projecting onto SPDs

    Projection on SPDs is not projecting onto SPDs

    Hi, nice to see another package doing optimizationon manifolds! I have not yet had the time to check this versus what pymanopt is doing (I think they use tensor flow as a backend, too?) But I just noticed that

    https://github.com/master/tensorflow-manopt/blob/93402f6770d5b3c45f232340fddfa92a7126f19a/tensorflow_manopt/manifolds/symmetric_positive.py#L37-L41

    This might be wrong. For SPDs, the characteristic property is, that all eigenvalues are positive, so this projection is not projection onto the manifold (of SPDs) but onto the set of positive semidefinite matrices. There is no projection onto the SPDs since that set is open in the set of (symmetric) matrices.

    opened by kellertuer 2
  • GrNet produces NaN entries in input tensor

    GrNet produces NaN entries in input tensor

    Hi! First of all, really appreciate you guys taking the time to build a much required riemmannian geometry based package in tensorflow. It is proving to be quite useful for me. However, I recently ran the [GrNet code] (https://github.com/master/tensorflow-riemopt/tree/master/examples/grnet) with the AFEW dataset(the default dataset used in the code) on my machine and it seems at some point the input tensors get filled with NaN values. I tried tinkering with the learning rate and a few other usual things that could determine the cause of such NaN value in a dl model but it seems to be of no use. Any idea as to why this might be the case- is the code still been checked for bugs or am I missing something? Thanks in advance!

    opened by SouvikBan 2
Releases(v0.1.1)
Owner
Oleg Smirnov
Oleg Smirnov
Randstad Artificial Intelligence Challenge (powered by VGEN). Soluzione proposta da Stefano Fiorucci (anakin87) - primo classificato

Randstad Artificial Intelligence Challenge (powered by VGEN) Soluzione proposta da Stefano Fiorucci (anakin87) - primo classificato Struttura director

Stefano Fiorucci 1 Nov 13, 2021
Large Scale Fine-Grained Categorization and Domain-Specific Transfer Learning. CVPR 2018

Large Scale Fine-Grained Categorization and Domain-Specific Transfer Learning Tensorflow code and models for the paper: Large Scale Fine-Grained Categ

Yin Cui 187 Oct 01, 2022
This project aim to create multi-label classification annotation tool to boost annotation speed and make it more easier.

This project aim to create multi-label classification annotation tool to boost annotation speed and make it more easier.

4 Aug 02, 2022
An implementation of the Contrast Predictive Coding (CPC) method to train audio features in an unsupervised fashion.

CPC_audio This code implements the Contrast Predictive Coding algorithm on audio data, as described in the paper Unsupervised Pretraining Transfers we

Meta Research 283 Dec 30, 2022
Interactive web apps created using geemap and streamlit

geemap-apps Introduction This repo demostrates how to build a multi-page Earth Engine App using streamlit and geemap. You can deploy the app on variou

Qiusheng Wu 27 Dec 23, 2022
Unoffical implementation about Image Super-Resolution via Iterative Refinement by Pytorch

Image Super-Resolution via Iterative Refinement Paper | Project Brief This is a unoffical implementation about Image Super-Resolution via Iterative Re

LiangWei Jiang 2.5k Jan 02, 2023
Unofficial pytorch implementation of paper "One-Shot Free-View Neural Talking-Head Synthesis for Video Conferencing"

One-Shot Free-View Neural Talking Head Synthesis Unofficial pytorch implementation of paper "One-Shot Free-View Neural Talking-Head Synthesis for Vide

ZLH 406 Dec 23, 2022
Efficient and intelligent interactive segmentation annotation software

Efficient and intelligent interactive segmentation annotation software

294 Dec 30, 2022
Predicting Axillary Lymph Node Metastasis in Early Breast Cancer Using Deep Learning on Primary Tumor Biopsy Slides

Predicting Axillary Lymph Node Metastasis in Early Breast Cancer Using Deep Learning on Primary Tumor Biopsy Slides Project | This repo is the officia

CVSM Group - email: <a href=[email protected]"> 33 Dec 28, 2022
MultiSiam: Self-supervised Multi-instance Siamese Representation Learning for Autonomous Driving

MultiSiam: Self-supervised Multi-instance Siamese Representation Learning for Autonomous Driving Code will be available soon. Motivation Architecture

Kai Chen 24 Apr 19, 2022
StyleGAN2-ADA - Official PyTorch implementation

Abstract: Training generative adversarial networks (GAN) using too little data typically leads to discriminator overfitting, causing training to diverge. We propose an adaptive discriminator augmenta

NVIDIA Research Projects 3.2k Dec 30, 2022
Contextual Attention Network: Transformer Meets U-Net

Contextual Attention Network: Transformer Meets U-Net Contexual attention network for medical image segmentation with state of the art results on skin

Reza Azad 67 Nov 28, 2022
A simple log parser and summariser for IIS web server logs

IISLogFileParser A basic parser tool for IIS Logs which summarises findings from the log file. Inspired by the Gist https://gist.github.com/wh13371/e7

2 Mar 26, 2022
CCCL: Contrastive Cascade Graph Learning.

CCGL: Contrastive Cascade Graph Learning This repo provides a reference implementation of Contrastive Cascade Graph Learning (CCGL) framework as descr

Xovee Xu 19 Dec 05, 2022
moving object detection for satellite videos.

DSFNet: Dynamic and Static Fusion Network for Moving Object Detection in Satellite Videos Algorithm Introduction DSFNet: Dynamic and Static Fusion Net

xiaochao 39 Dec 16, 2022
Using Machine Learning to Test Causal Hypotheses in Conjoint Analysis

Readme File for "Using Machine Learning to Test Causal Hypotheses in Conjoint Analysis" by Ham, Imai, and Janson. (2022) All scripts were written and

0 Jan 27, 2022
Official codebase for ICLR oral paper Unsupervised Vision-Language Grammar Induction with Shared Structure Modeling

CLIORA This is the official codebase for ICLR oral paper: Unsupervised Vision-Language Grammar Induction with Shared Structure Modeling. We introduce

Bo Wan 32 Dec 23, 2022
SemEval2022 Patronizing and Condescending Language (PCL) Detection

SemEval2022 Patronizing and Condescending Language (PCL) Detection This task is from SemEval 2022. What is Patronizing and Condescending Language (PCL

Daniel Saeedi 0 Aug 05, 2022
YOLOv2 in PyTorch

YOLOv2 in PyTorch NOTE: This project is no longer maintained and may not compatible with the newest pytorch (after 0.4.0). This is a PyTorch implement

Long Chen 1.5k Jan 02, 2023
Recognize Handwritten Digits using Deep Learning on the browser itself.

MNIST on the Web An attempt to predict MNIST handwritten digits from my PyTorch model from the browser (client-side) and not from the server, with the

Harjyot Bagga 7 May 28, 2022