RESEARCH

Riemannian Continuous Normalizing Flows

December 6, 2020

Abstract

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, tori, and hyperbolic spaces, most normalizing flows implicitly assume a flat geometry, making them either misspecified or ill-suited in these situations. To overcome this problem, we introduce Riemannian continuous normalizing flows, a model which admits the parametrization of flexible probability measures on smooth manifolds by defining flows as the solution to ordinary differential equations. We show that this approach can lead to substantial improvements on both synthetic and real-world data when compared to standard flows or previously introduced projected flows.

Download the Paper

AUTHORS

Written by

Emile Mathieu

Maximilian Nickel

Research Topics

Core Machine Learning

Related Publications

May 17, 2019

COMPUTER VISION

SPEECH & AUDIO

GLoMo: Unsupervised Learning of Transferable Relational Graphs | Facebook AI Research

Modern deep transfer learning approaches have mainly focused on learning generic feature vectors from one task that are transferable to other tasks, such as word embeddings in language and pretrained convolutional features in vision. However,…

Zhilin Yang, Jake (Junbo) Zhao, Bhuwan Dhingra, Kaiming He, William W. Cohen, Ruslan Salakhutdinov, Yann LeCun

May 17, 2019

May 06, 2019

COMPUTER VISION

NLP

No Training Required: Exploring Random Encoders for Sentence Classification | Facebook AI Research

We explore various methods for computing sentence representations from pre-trained word embeddings without any training, i.e., using nothing but random parameterizations. Our aim is to put sentence embeddings on more solid footing by 1) looking…

John Wieting, Douwe Kiela

May 06, 2019

May 06, 2019

NLP

COMPUTER VISION

Efficient Lifelong Learning with A-GEM | Facebook AI Research

In lifelong learning, the learner is presented with a sequence of tasks, incrementally building a data-driven prior which may be leveraged to speed up learning of a new task. In this work, we investigate the efficiency of current lifelong…

Arslan Chaudhry, Marc'Aurelio Ranzato, Marcus Rohrbach, Mohamed Elhoseiny

May 06, 2019

May 06, 2019

COMPUTER VISION

Learning Exploration Policies for Navigation | Facebook AI Research

Numerous past works have tackled the problem of task-driven navigation. But, how to effectively explore a new environment to enable a variety of down-stream tasks has received much less attention. In this work, we study how agents can…

Tao Chen, Saurabh Gupta, Abhinav Gupta

May 06, 2019

Help Us Pioneer The Future of AI

We share our open source frameworks, tools, libraries, and models for everything from research exploration to large-scale production deployment.