# Learning Deep ResNet Blocks Sequentially using Boosting Theory

Author Huang, Furong · Ash, Jordan · Langford, John · Schapire, Robert 2017 See all Details

#### Abstract

Deep neural networks are known to be difficult to train due to the instability of back-propagation. A deep \emph{residual network} (ResNet) with identity loops remedies this by stabilizing gradient computations. We prove a boosting theory for the ResNet architecture. We construct $T$ weak module classifiers, each contains two of the $T$ layers, such that the combined strong learner is a ResNet. Therefore, we introduce an alternative Deep ResNet training algorithm, \emph{BoostResNet}, which is particularly suitable in non-differentiable architectures. Our proposed algorithm merely requires a sequential training of $T$ "shallow ResNets" which are inexpensive. We prove that the training error decays exponentially with the depth $T$ if the \emph{weak module classifiers} that we train perform slightly better than some weak baseline. In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition. Our results apply to general multi-class ResNets. A generalization error bound based on margin theory is proved and suggests ResNet's resistant to overfitting under network with $l_1$ norm bounded weights.

### Details

Title Learning Deep ResNet Blocks Sequentially using Boosting Theory Huang, Furong · Ash, Jordan · Langford, John · Schapire, Robert 2017 Research Article eng 2017-06-15 00:00:00 Learning
This is Version 1 of this record. We added this version on June 17, 2017. This version is based on an original data import from arXiv.org e-Print archive.