Mohammad Pezeshki

Multi-scale Feature Learning Dynamics: Insights for Double Descent

A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting fro… (see more)m the high-dimensional interactions between the large number of network parameters. Such non-trivial dynamics lead to intriguing behaviors such as the phenomenon of "double descent" of the generalization error. The more commonly studied aspect of this phenomenon corresponds to model-wise double descent where the test error exhibits a second descent with increasing model complexity, beyond the classical U-shaped error curve. In this work, we investigate the origins of the less studied epoch-wise double descent in which the test error undergoes two non-monotonous transitions, or descents as the training time increases. By leveraging tools from statistical physics, we study a linear teacher-student setup exhibiting epoch-wise double descent similar to that in deep neural networks. In this setting, we derive closed-form analytical expressions for the evolution of generalization error over training. We find that double descent can be attributed to distinct features being learned at different scales: as fast-learning features overfit, slower-learning features start to fit, resulting in a second descent in test error. We validate our findings through numerical experiments where our theory accurately predicts empirical findings and remains consistent with observations in deep neural networks.

2022-06-27

Proceedings of the 39th International Conference on Machine Learning (published)

doi.org

proceedings.mlr.press

Gradient Starvation: A Learning Proclivity in Neural Networks

Sékou-Oumar Kaba

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks… (see more). Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

2021-11-08

NeurIPS.cc/2021/Conference (poster)

doi.org

openreview.net

Negative Momentum for Improved Game Dynamics

Gauthier Gidel

Reyhane Askari Hemmat

Rémi Le Priol

Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiab… (see more)le games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial networks (GANs) and actor-critic systems. However, compared to single-objective optimization, game dynamics are more complex and less understood. In this paper, we analyze gradient-based methods with momentum on simple games. We prove that alternating updates are more stable than simultaneous updates. Next, we show both theoretically and empirically that alternating gradient updates with a negative momentum term achieves convergence in a difficult toy adversarial problem, but also on the notoriously difficult to train saturating GANs.

2019-04-10

Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics (published)

doi.org

proceedings.mlr.press

Convergence Properties of Deep Neural Networks on Separable Data

Remi Tachet des Combes

Mohammad Pezeshki

Samira Shabanian

Aaron Courville

Yoshua Bengio

While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely… (see more) misunderstood. In this work, we study the case of binary classification and prove various properties of learning in such networks under strong assumptions such as linear separability of the data. Extending existing results from the linear case, we confirm empirical observations by proving that the classification error also follows a sigmoidal shape in nonlinear architectures. We show that given proper initialization, learning expounds parallel independent modes and that certain regions of parameter space might lead to failed training. We also demonstrate that input norm and features’ frequency in the dataset lead to distinct convergence speeds which might shed some light on the generalization capabilities of deep neural networks. We provide a comparison between the dynamics of learning with cross-entropy and hinge losses, which could prove useful to understand recent progress in the training of generative adversarial networks. Finally, we identify a phenomenon that we baptize gradient starvation where the most frequent features in a dataset prevent the learning of other less frequent but equally informative features.

2018-09-26

(published)

openreview.net

On the Learning Dynamics of Deep Neural Networks

Remi Tachet des Combes

Mohammad Pezeshki

Samira Shabanian

Aaron Courville

Yoshua Bengio

While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely… (see more) misunderstood. In this work, we study the case of binary classification and prove various properties of learning in such networks under strong assumptions such as linear separability of the data. Extending existing results from the linear case, we confirm empirical observations by proving that the classification error also follows a sigmoidal shape in nonlinear architectures. We show that given proper initialization, learning expounds parallel independent modes and that certain regions of parameter space might lead to failed training. We also demonstrate that input norm and features' frequency in the dataset lead to distinct convergence speeds which might shed some light on the generalization capabilities of deep neural networks. We provide a comparison between the dynamics of learning with cross-entropy and hinge losses, which could prove useful to understand recent progress in the training of generative adversarial networks. Finally, we identify a phenomenon that we baptize \textit{gradient starvation} where the most frequent features in a dataset prevent the learning of other less frequent but equally informative features.

2018-09-17

ArXiv (preprint)

arxiv.org

Towards End-to-End Speech Recognition with Deep Convolutional Neural Networks

Convolutional Neural Networks (CNNs) are effective models for reducing spectral variations and modeling spectral correlations in acoustic fe… (see more)atures for automatic speech recognition (ASR). Hybrid speech recognition systems incorporating CNNs with Hidden Markov Models/Gaussian Mixture Models (HMMs/GMMs) have achieved the state-of-the-art in various benchmarks. Meanwhile, Connectionist Temporal Classification (CTC) with Recurrent Neural Networks (RNNs), which is proposed for labeling unsegmented sequences, makes it feasible to train an end-to-end speech recognition system instead of hybrid settings. However, RNNs are computationally expensive and sometimes difficult to train. In this paper, inspired by the advantages of both CNNs and the CTC approach, we propose an end-to-end speech framework for sequence labeling, by combining hierarchical CNNs with CTC directly without recurrent connections. By evaluating the approach on the TIMIT phoneme recognition task, we show that the proposed model is not only computationally efficient, but also competitive with the existing baseline systems. Moreover, we argue that CNNs have the capability to model temporal correlations with appropriate context information.

2016-09-07

Interspeech 2016 (published)

doi.org

arxiv.org

Deconstructing the Ladder Network Architecture

Linxi Fan

The Manual labeling of data is and will remain a costly endeavor. For this reason, semi-supervised learning remains a topic of practical imp… (see more)ortance. The recently proposed Ladder Network is one such approach that has proven to be very successful. In addition to the supervised objective, the Ladder Network also adds an unsupervised objective corresponding to the reconstruction costs of a stack of denoising autoencoders. Although the empirical results are impressive, the Ladder Network has many components intertwined, whose contributions are not obvious in such a complex architecture. In order to help elucidate and disentangle the different ingredients in the Ladder Network recipe, this paper presents an extensive experimental investigation of variants of the Ladder Network in which we replace or remove individual components to gain more insight into their relative importance. We find that all of the components are necessary for achieving optimal performance, but they do not contribute equally. For semi-supervised tasks, we conclude that the most important contribution is made by the lateral connection, followed by the application of noise, and finally the choice of what we refer to as the `combinator function' in the decoder path. We also find that as the number of labeled training examples increases, the lateral connections and reconstruction criterion become less important, with most of the improvement in generalization being due to the injection of noise in each layer. Furthermore, we present a new type of combinator function that outperforms the original design in both fully- and semi-supervised tasks, reducing record test error rates on Permutation-Invariant MNIST to 0.57% for the supervised setting, and to 0.97% and 1.0% for semi-supervised settings with 1000 and 100 labeled examples respectively.

2016-06-10

Proceedings of The 33rd International Conference on Machine Learning (published)

doi.org

proceedings.mlr.press

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

Zoneout: Regularizing RNNs by Randomly Preserving Hidden Activations

David Krueger

Nan Rosemary Ke

Christopher Pal

We propose zoneout, a novel method for regularizing RNNs. At each timestep, zoneout stochastically forces some hidden units to maintain thei… (see more)r previous values. Like dropout, zoneout uses random noise to train a pseudo-ensemble, improving generalization. But by preserving instead of dropping hidden units, gradient information and state information are more readily propagated through time, as in feedforward stochastic depth networks. We perform an empirical investigation of various RNN regularizers, and find that zoneout gives significant performance improvements across tasks. We achieve competitive results with relatively simple models in character- and word-level language modelling on the Penn Treebank and Text8 datasets, and combining with recurrent batch normalization yields state-of-the-art results on permuted sequential MNIST.

2015-12-31

arXiv (preprint)

doi.org

arxiv.org

Mila Ventures Founder in Residence

TRAIL: Responsible AI for Professionals and Leaders

AI Advantage: Productivity in Public Service

Mohammad Pezeshki

Publications

Mila Ventures Founder in Residence

TRAIL: Responsible AI for Professionals and Leaders

AI Advantage: Productivity in Public Service

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Mohammad Pezeshki

Publications