Learning Deep ResNet Blocks Sequentially using Boosting Theory - Huang, Furon; Ash, Jordan; Langford, John; Schapire, Robert E. (ICML 2018, 2018)
Deep neural networks are known to be difficult to train due to the instability of back-propagation. A deep [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, [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 [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 l1 norm bounded weights.