Batch Normalization (BN) is ubiquitously employed for accelerating neural
network training and improving the generalization capability by performing
standardization within mini-batches. Decorrelated Batch Normalization (DBN)
further boosts the above effectiveness by whitening. However, DBN relies
heavily on either a large batch size, or eigen-decomposition that suffers from
poor efficiency on GPUs. We propose Iterative Normalization (IterNorm), which
employs Newton's iterations for much more efficient whitening, while
simultaneously avoiding the eigen-decomposition. Furthermore, we develop a
comprehensive study to show IterNorm has better trade-off between optimization
and generalization, with theoretical and experimental support. To this end, we
exclusively introduce Stochastic Normalization Disturbance (SND), which
measures the inherent stochastic uncertainty of samples when applied to
normalization operations. With the support of SND, we provide natural
explanations to several phenomena from the perspective of optimization, e.g.,
why group-wise whitening of DBN generally outperforms full-whitening and why
the accuracy of BN degenerates with reduced batch sizes. We demonstrate the
consistently improved performance of IterNorm with extensive experiments on
CIFAR-10 and ImageNet over BN and DBN.

本文提出了一种新的神经网络训练方法：Iterative Normalization，通过牛顿迭代实现高效且无矩阵分解的白化，同时引入 Stochastic Normalization Disturbance，增加实验的稳定性，实验表明 IterNorm 具有更好的优化与泛化折衷。

迭代归一化：从标准化走向高效白化

Iterative Normalization: Beyond Standardization towards Efficient  Whitening

Batch Normalization (BN) is capable of accelerating the training of deep
models by centering and scaling activations within mini-batches. In this work,
we propose Decorrelated Batch Normalization (DBN), which not just centers and
scales activations but whitens them. We explore multiple whitening techniques,
and find that PCA whitening causes a problem we call stochastic axis swapping,
which is detrimental to learning. We show that ZCA whitening does not suffer
from this problem, permitting successful learning. DBN retains the desirable
qualities of BN and further improves BN's optimization efficiency and
generalization ability. We design comprehensive experiments to show that DBN
can improve the performance of BN on multilayer perceptrons and convolutional
neural networks. Furthermore, we consistently improve the accuracy of residual
networks on CIFAR-10, CIFAR-100, and ImageNet.

本文提出了一种新的批量标准化方法 Decorrelated Batch Normalization（DBN），不仅可以中心化和缩放激活，还可以白化激活，通过多种白化技术的探索发现 ZCA 白化可以成功学习并且可以提高 BN 的性能和优化效率，具有双重优势。我们通过一系列实验展示了 DBN 改进了 BN 的性能并且在多层感知器和卷积神经网络上都可以提高准确性，还在 CIFAR-10、CIFAR-100 和 ImageNet 数据集上增加了残余网络的准确率。