Laurent Dinh

Solving ODE with Universal Flows: Approximation Theory for Flow-Based Models

Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that al… (see more)lows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.

2020-02-25

International Conference on Learning Representations (published)

openreview.net

Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models

Chin-wei Huang

Laurent Dinh

Aaron Courville

In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drasticall… (see more)y increasing the computational cost of sampling and evaluation of a lower bound on the likelihood. Theoretically, we prove the proposed flow can approximate a Hamiltonian ODE as a universal transport map. Empirically, we demonstrate state-of-the-art performance on standard benchmarks of flow-based generative modeling.

2020-02-16

ArXiv (preprint)

arxiv.org

Learnable Explicit Density for Continuous Latent Space and Variational Inference

In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its correspon… (see more)ding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and inference. Second, we analyze the family of inverse autoregressive flows (inverse AF) and show that with further improvement, inverse AF could be used as universal approximation to any complicated posterior. Our analysis results in a unified approach to parameterizing a VAE, without the need to restrict ourselves to use factorial Gaussians in the latent real space.

2017-10-05

ArXiv (preprint)

arxiv.org

Theano: A Python framework for fast computation of mathematical expressions

Rami Al-Rfou

Guillaume Alain

Amjad Almahairi

Christof Angermueller

Dzmitry Bahdanau

Nicolas Ballas

Frédéric Bastien

Justin Bayer

Anatoly Belikov

Alexander Belopolsky

Josh Bleecher Snyder

Nicolas Boulanger-Lewandowski

Xavier Bouthillier

Alexandre De Brébisson

Olivier Breuleux … (see 92 more)

Pierre-Luc Carrier

Paul Christiano

Myriam Côté

Yann N. Dauphin

Julien Demouth

Sander Dieleman

Samira Ebrahimi Kahou

Ziye Fan

Mathieu Germain

Matt Graham

Balázs Hidasi

Arjun Jain

Kai Jia

Mikhail Korobov

Vivek Kulkarni

Alex Lamb

Pascal Lamblin

Eric Larsen

César Laurent

Sean Lee

Simon Lefrancois

Simon Lemieux

Nicholas Léonard

Zhouhan Lin

Jesse A. Livezey

Cory Lorenz

Jeremiah Lowin

Qianli Ma

Pierre-Antoine Manzagol

Robert T. McGibbon

Mehdi Mirza

Alberto Orlandi

Christopher Pal

Razvan Pascanu

Mohammad Pezeshki

Colin Raffel

Daniel Renshaw

Matthew Rocklin

Adriana Romero

Markus Roth

Peter Sadowski

John Salvatier

François Savard

Jan Schlüter

John Schulman

Gabriel Schwartz

Iulian Vlad Serban

Dmitriy Serdyuk

Samira Shabanian

Etienne Simon

Sigurd Spieckermann

S. Ramana Subramanyam

Gijs van Tulder

Sebastian Urban

Dustin J. Webb

Matthew Willson

Lijun Xue

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficie… (see more)ntly. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

2015-12-31

arXiv (preprint)

doi.org

arxiv.org

TRAIL: Responsible AI for Professionals and Leaders

Mila Ventures Founder in Residence

AI Advantage: Productivity in Public Service

Laurent Dinh

Publications

TRAIL: Responsible AI for Professionals and Leaders

Mila Ventures Founder in Residence

AI Advantage: Productivity in Public Service

Popular keywords:

Laurent Dinh

Publications