Standardizing input vectors to have zero mean and unit variance not only places parameters on a similar a priori scale to aid optimizers, but it also constrains the complexity of the functions that act upon them. For instance, theoretical bounds such as the radius-margin bound in support vector machines and the Perceptron Convergence Theorem explicitly rely on the inputs having a bounded norm.

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Normalization of training data may help reducing the bias and variance, and speeds up Gradient Descent, and consequently, training of the deep learning model, as shown in the figure.

Normalization Helps Deep Learning

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Feature scaling greatly affects which of the following supervised machine learning methods? 

Feature Standardization and Function Complexity

Batch normalization is a technique designed to accelerate and stabilize the training of deep neural networks. Mechanistically, it centers and rescales the intermediate layer activations back to a controlled mean and variance, preventing their distributions from diverging across layers and over time. By keeping these intermediate values on a comparable scale, batch normalization enables the use of more aggressive learning rates. The technique was originally motivated by the concept of covariate shift applied to internal layers, but the hypothesis that it works by reducing this so-called internal covariate shift has since been challenged and does not appear to be a valid explanation for its effectiveness. Although intuitively thought to make the optimization landscape smoother, the precise mechanism by which batch normalization aids training remains an open research question. Despite this theoretical uncertainty, batch normalization has proven indispensable in practice, being applied in nearly all deployed image classifiers and earning the original paper tens of thousands of citations.

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