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Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Sergey Ioffe, +1 more
- 11 Feb 2015 - 
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TLDR
Batch Normalization as mentioned in this paper normalizes layer inputs for each training mini-batch to reduce the internal covariate shift in deep neural networks, and achieves state-of-the-art performance on ImageNet.
Abstract: 
Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.

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References
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Proceedings Article

On the importance of initialization and momentum in deep learning

TL;DR: It is shown that when stochastic gradient descent with momentum uses a well-designed random initialization and a particular type of slowly increasing schedule for the momentum parameter, it can train both DNNs and RNNs to levels of performance that were previously achievable only with Hessian-Free optimization.
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Large Scale Distributed Deep Networks

TL;DR: This paper considers the problem of training a deep network with billions of parameters using tens of thousands of CPU cores and develops two algorithms for large-scale distributed training, Downpour SGD and Sandblaster L-BFGS, which increase the scale and speed of deep network training.
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Improving predictive inference under covariate shift by weighting the log-likelihood function

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Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

TL;DR: In this paper, the authors show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions.
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