In recent years, state-of-the-art methods in computer vision have utilized
increasingly deep convolutional neural network architectures (CNNs), with some
of the most successful models employing hundreds or even thousands of layers. A
variety of pathologies such as vanishing/exploding gradients make training such
deep networks challenging. While residual connections and batch normalization
do enable training at these depths, it has remained unclear whether such
specialized architecture designs are truly necessary to train deep CNNs. In
this work, we demonstrate that it is possible to train vanilla CNNs with ten
thousand layers or more simply by using an appropriate initialization scheme.
We derive this initialization scheme theoretically by developing a mean field
theory for signal propagation and by characterizing the conditions for
dynamical isometry, the equilibration of singular values of the input-output
Jacobian matrix. These conditions require that the convolution operator be an
orthogonal transformation in the sense that it is norm-preserving. We present
an algorithm for generating such random initial orthogonal convolution kernels
and demonstrate empirically that they enable efficient training of extremely
deep architectures.
Description
[1806.05393] Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks
%0 Journal Article
%1 xiao2018dynamical
%A Xiao, Lechao
%A Bahri, Yasaman
%A Sohl-Dickstein, Jascha
%A Schoenholz, Samuel S.
%A Pennington, Jeffrey
%D 2018
%K bayesian mean-field
%T Dynamical Isometry and a Mean Field Theory of CNNs: How to Train
10,000-Layer Vanilla Convolutional Neural Networks
%U http://arxiv.org/abs/1806.05393
%X In recent years, state-of-the-art methods in computer vision have utilized
increasingly deep convolutional neural network architectures (CNNs), with some
of the most successful models employing hundreds or even thousands of layers. A
variety of pathologies such as vanishing/exploding gradients make training such
deep networks challenging. While residual connections and batch normalization
do enable training at these depths, it has remained unclear whether such
specialized architecture designs are truly necessary to train deep CNNs. In
this work, we demonstrate that it is possible to train vanilla CNNs with ten
thousand layers or more simply by using an appropriate initialization scheme.
We derive this initialization scheme theoretically by developing a mean field
theory for signal propagation and by characterizing the conditions for
dynamical isometry, the equilibration of singular values of the input-output
Jacobian matrix. These conditions require that the convolution operator be an
orthogonal transformation in the sense that it is norm-preserving. We present
an algorithm for generating such random initial orthogonal convolution kernels
and demonstrate empirically that they enable efficient training of extremely
deep architectures.
@article{xiao2018dynamical,
abstract = {In recent years, state-of-the-art methods in computer vision have utilized
increasingly deep convolutional neural network architectures (CNNs), with some
of the most successful models employing hundreds or even thousands of layers. A
variety of pathologies such as vanishing/exploding gradients make training such
deep networks challenging. While residual connections and batch normalization
do enable training at these depths, it has remained unclear whether such
specialized architecture designs are truly necessary to train deep CNNs. In
this work, we demonstrate that it is possible to train vanilla CNNs with ten
thousand layers or more simply by using an appropriate initialization scheme.
We derive this initialization scheme theoretically by developing a mean field
theory for signal propagation and by characterizing the conditions for
dynamical isometry, the equilibration of singular values of the input-output
Jacobian matrix. These conditions require that the convolution operator be an
orthogonal transformation in the sense that it is norm-preserving. We present
an algorithm for generating such random initial orthogonal convolution kernels
and demonstrate empirically that they enable efficient training of extremely
deep architectures.},
added-at = {2020-03-25T02:43:12.000+0100},
author = {Xiao, Lechao and Bahri, Yasaman and Sohl-Dickstein, Jascha and Schoenholz, Samuel S. and Pennington, Jeffrey},
biburl = {https://www.bibsonomy.org/bibtex/222a8a1ab3efffbcb6bfcaa1727e151c3/kirk86},
description = {[1806.05393] Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks},
interhash = {5d16f0bc9e38172546481ed95e0d6399},
intrahash = {22a8a1ab3efffbcb6bfcaa1727e151c3},
keywords = {bayesian mean-field},
note = {cite arxiv:1806.05393Comment: ICML 2018 Conference Proceedings},
timestamp = {2020-03-25T02:43:12.000+0100},
title = {Dynamical Isometry and a Mean Field Theory of CNNs: How to Train
10,000-Layer Vanilla Convolutional Neural Networks},
url = {http://arxiv.org/abs/1806.05393},
year = 2018
}