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arXiv:1502.03167cs.LG

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

Sergey Ioffe, Christian Szegedy

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.

arXiv comments
Journal reference
DOI
Subjects
cs.LGMachine Learning

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Linked by 4 identifiable commenters in 5 comments across 5 threads, from May 2015 to Jun 2023. Found in 3 HN submissions from Feb 2015 to Feb 2026. Open submission discussions.

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Discussed in comments5 threads

  1. Neural networks in the 1990s 1 comment
    • We were missing two architecture patterns that were needed to get deeper nets to converge: residual nets [1] which solved gradient propagation, and batch normalization [2] which solved initialization. [1] Residual nets (2015): https://arxiv.org/abs/1512.03385 [2] Batch…

      radqView on HNParent context

    • I think they're referring to the momentum parameter at [1]. The exponential moving average (EMA) of the batch mean/variance is used in the batch normalizing transform (Algorithm 1 in [2]). The momentum ranges from 0 to 1. If it's close to 1, which the default of 0.99 is, the EMA…

      walrusView on HNParent context

    • Good list! I think it's important to note that this article is (intentionally) focused on modern CNN architectures, and not "deep learning" in general. I'd also add in the following "technique" articles: Geoff Hinton et al.'s dropout paper[0] and Loffe and Szegedy's Batch…

      sjaView on HNParent context

    • I'm not qualified to answer this, but I will anyway. To "operate" neural networks (as opposed to writing a framework for them), you need to know the building blocks. There are basic blocks like fully connected layers, convolutions, and nonlinear activations. Beyond those, there…

      walrusView on HNParent context

    • http://image-net.org/challenges/LSVRC/2012/results.html One team at 15% http://www.image-net.org/challenges/LSVRC/2014/results Most teams are below 15%, GooLeNet is at 6% http://www.image-net.org/challenges/LSVRC/2014/results Microsoft is now below 5%…

      twelfthnightView on HNParent context

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