Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. That means BN can be explained in terms of kernels that naturally emerge from the probability density function of the underlying data distribution. However, given the rectifying non-linearities employed in CNN architectures, distribution of inputs to the layers show heavy tail and asymmetric characteristics. Therefore, we propose approximating underlying data distribution not with one, but a mixture of Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM), reveals that BN can be improved by independently normalizing with respect to the statistics of disentangled sub-populations. We refer to our proposed soft piecewise version of BN as Mixture Normalization (MN). Through extensive set of experiments on CIFAR-10 and CIFAR-100, we show that MN not only effectively accelerates training image classification and Generative Adversarial networks, but also reaches higher quality models.

该研究使用 Fisher 核的角度探索 Batch Normalization的优化，提出了一种新的 Mixture Normalization 方法，通过 CIFAR-10 和 CIFAR-100 实验验证能够有效加速深度神经网络模型的训练

通过批量归一化模型中分离变化模式以加速训练