Razvan Pascanu

Predicting Unreliable Predictions by Shattering a Neural Network

Andrea Vedaldi

Balaji Lakshminarayanan

Piecewise linear neural networks can be split into subfunctions, each with its own activation pattern, domain, and empirical error. Empirica… (voir plus)l error for the full network can be written as an expectation over empirical error of subfunctions. Constructing a generalization bound on subfunction empirical error indicates that the more densely a subfunction is surrounded by training samples in representation space, the more reliable its predictions are. Further, it suggests that models with fewer activation regions generalize better, and models that abstract knowledge to a greater degree generalize better, all else equal. We propose not only a theoretical framework to reason about subfunction error bounds but also a pragmatic way of approximately evaluating it, which we apply to predicting which samples the network will not successfully generalize to. We test our method on detection of misclassiﬁcation and out-of-distribution samples, ﬁnding that it performs competitively in both cases. In short, some network activation patterns are associated with higher reliability than others, and these can be identiﬁed using subfunction error bounds.

2021-01-01

arXiv.org (prépublication)

openreview.net

Theano: A Python framework for fast computation of mathematical expressions

Rami Al-rfou'

Guillaume Alain

Amjad Almahairi

Christof Angermüller

Dzmitry Bahdanau

Nicolas Ballas

Frédéric Bastien

Justin S. Bayer

A. Belikov

A. Belopolsky

Josh Bleecher Snyder

Nicolas Boulanger-Lewandowski

Xavier Bouthillier

Alexandre De Brébisson

Olivier Breuleux … (voir 92 de plus)

Paul F. Christiano

Myriam Côté

Julien Demouth

Sander Dieleman

M'elanie Ducoffe

Samira Ebrahimi Kahou

Dumitru Erhan

Ziye Fan

Orhan Firat

Mathieu Germain

Xavier Glorot

Ian G Goodfellow

Matthew Graham

Balázs Hidasi

Arjun Jain

Kai Jia

Mikhail V. Korobov

Vivek Kulkarni

Alex Lamb

Pascal Lamblin

Eric Larsen

César Laurent

S. Lee

Simon-mark Lefrancois

Simon Lemieux

Nicholas Léonard

Zhouhan Lin

J. Livezey

Cory R. Lorenz

Jeremiah L. Lowin

Qianli M. Ma

Pierre-Antoine Manzagol

R. McGibbon

Mehdi Mirza

Alberto Orlandi

Chris Pal

Razvan Pascanu

Mohammad Pezeshki

Colin Raffel

Daniel Renshaw

Matthew David Rocklin

Adriana Romero Soriano

Markus Dr. Roth

Peter Sadowski

John Salvatier

François Savard

Jan Schlüter

John D. Schulman

Gabriel Schwartz

Iulian V. Serban

Dmitriy Serdyuk

Samira Shabanian

Etienne Simon

Sigurd Spieckermann

S. Subramanyam

Gijs van Tulder

Sebastian Urban

Dustin J. Webb

M. Willson

Lijun Xue

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficie… (voir plus)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.

2016-05-09

ArXiv (prépublication)

arxiv.org

Theano: A Python framework for fast computation of mathematical expressions

Rami Al-rfou'

Guillaume Alain

Amjad Almahairi

Christof Angermüller

Dzmitry Bahdanau

Nicolas Ballas

Frédéric Bastien

Justin S. Bayer

A. Belikov

A. Belopolsky

J. Bergstra

Josh Bleecher Snyder

Nicolas Boulanger-Lewandowski

Xavier Bouthillier

Alexandre De Brébisson

Olivier Breuleux … (voir 92 de plus)

Paul F. Christiano

Myriam Côté

Julien Demouth

Sander Dieleman

M'elanie Ducoffe

Samira Ebrahimi Kahou

Dumitru Erhan

Ziye Fan

Orhan Firat

Mathieu Germain

Xavier Glorot

Ian J. Goodfellow

Matthew Graham

Balázs Hidasi

Arjun Jain

S'ebastien Jean

Kai Jia

Mikhail V. Korobov

Vivek Kulkarni

Alex Lamb

Pascal Lamblin

Eric P. Larsen

César Laurent

S. Lee

Simon-mark Lefrancois

Simon Lemieux

Nicholas Léonard

Zhouhan Lin

J. Livezey

Cory R. Lorenz

Jeremiah L. Lowin

Qianli M. Ma

Pierre-Antoine Manzagol

R. McGibbon

Mehdi Mirza

Alberto Orlandi

Chris Pal

Razvan Pascanu

Mohammad Pezeshki

Colin Raffel

Daniel Renshaw

Matthew David Rocklin

Adriana Romero Soriano

Markus Dr. Roth

Peter Sadowski

John Salvatier

François Savard

Jan Schlüter

John D. Schulman

Gabriel Schwartz

Iulian V. Serban

Dmitriy Serdyuk

Samira Shabanian

Etienne Simon

Sigurd Spieckermann

S. Subramanyam

Jakub Sygnowski

Jeremie Tanguay

Gijs van Tulder

Joseph P. Turian

Sebastian Urban

Dustin J. Webb

M. Willson

Lijun Xue

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficie… (voir plus)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.

2016-05-09

ArXiv (preprint)

arxiv.org

Theano: Deep Learning on GPUs with Python

Frédéric Bastien

Pascal Lamblin

Ian G Goodfellow

In this paper, we present Theano 1 , a framework in the Python programming language for defining, optimizing and evaluating expressions invo… (voir plus)lving high-level operations on tensors. Theano offers most of NumPy’s functionality, but adds automatic symbolic differentiation, GPU support, and faster expression evaluation. Theano is a general mathematical tool, but it was developed with the goal of facilitating research in deep learning. The Deep Learning Tutorials 2 introduce recent advances in deep learning, and showcase how Theano

2012-01-01

(publié)

www.semanticscholar.org

Theano: A CPU and GPU Math Compiler in Python

James Bergstra

Olivier Breuleux

Frédéric Bastien

Pascal Lamblin

Joseph P. Turian

Theano is a compiler for mathematical expressions in Python that combines the convenience of NumPy's syntax with the speed of optimized nati… (voir plus)ve machine language. The user composes mathematical expressions in a high-level description that mimics NumPy's syntax and semantics, while being statically typed and functional (as opposed to imperative). These expressions allow Theano to provide symbolic differentiation. Before performing computation, Theano optimizes the choice of expressions, translates them into C++ (or CUDA for GPU), compiles them into dynamically loaded Python modules, all automatically. Common machine learn- ing algorithms implemented with Theano are from 1:6 to 7:5 faster than competitive alternatives (including those implemented with C/C++, NumPy/SciPy and MATLAB) when compiled for the CPU and between 6:5 and 44 faster when compiled for the GPU. This paper illustrates how to use Theano, outlines the scope of the compiler, provides benchmarks on both CPU and GPU processors, and explains its overall design.

2010-01-01

SciPy (publié)

doi.org

Theano: A CPU and GPU Math Compiler in Python

James Bergstra

Olivier Breuleux

Frédéric Bastien

Pascal Lamblin