Since we normalize the inputs in each layer, the changes in the previous layer won't have much influence on the next layer. This is because, it reduces the amount of shift in the distribution of inputs to each layer (covariate shifts).

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- It makes your hyperparameter search problem much easier.
- It makes the neural network more robust to the choice of hyperparameters in a much bigger range of hyperparameters.
- It makes training even very deep networks easier.
- It has a slight regularization effect.

Benefits of Batch Norm in Deep Learning

Covariate shift is a category of distribution shift where the marginal distribution of the input features (covariates) changes over time, while the conditional distribution of the labels given the inputs, $$P(y \mid \mathbf{x})$$, remains constant. It is the most natural assumption to make in settings where the input features $$\mathbf{x}$$ are believed to cause the label $$y$$. An example of covariate shift is training a classifier to distinguish cats and dogs using real photographs, but testing it exclusively on cartoon images.

Covariate Shift

Dive into Deep Learning

Why do we normalize the inputs X in Deep Learning?

In one hypothesis, it helps to eliminate internal covariate shifts.

Visualization of How Batch Norm Helps Speed up Deep Learning

Batch Norm Makes Training Deep Networks Easier

Batch Norm has a slight regularization effect. Since we shift and scale *z* based on the mean and variance of only a single batch, it adds some noise into each hidden layer activation. So like dropout, it will add noise to each hidden layer’s activation. However, the effect is so small that we might want to use it together with other regularization methods like dropout.
If one uses a larger mini-batch size, it'd create less noise and thereby reduce the regularization effect. 

Batch Norm as Regularization in Deep Learning

Normalizing the outputs of layers in deep neural networks—by subtracting the mean and dividing by the standard deviation—helps to effectively mitigate the covariate shift problem. This reduction in covariate shift is a primary mechanism by which layer normalization improves overall training stability.

Reduction of Covariate Shift via Layer Normalization

Sampling bias during data collection can result in severe covariate shift, leading to models that fail in practice. For example, a medical algorithm designed to detect a disease using blood samples might be trained on a dataset consisting of sick older patients alongside healthy college students. Because the cohorts differ drastically in unrelated factors like age and hormone levels, the classifier might achieve high accuracy by learning these spurious features instead of genuine disease indicators. When deployed on real patients, the test will likely fail due to the extreme covariate shift between the training sample and the actual patient population.

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