Batch Normalization

Batch Normalization is a methodology employed in Deep Learning to enhance the efficiency of neural networks. During the training of a neural network, the model's weights are modified based on input data to optimize prediction accuracy. However, as training progresses, the output distribution of each layer can fluctuate, complicating the training process.

This is where Batch Normalization comes into play. It standardizes the output from each layer to ensure that values have a mean close to 0 and a standard deviation near 1. The normalization process is executed using the formula:

Normalization Formula

Mini-Batches

The normalization occurs within small subsets of data termed "mini-batches." This approach is necessary because processing the entire dataset simultaneously is often impractical due to memory and computational constraints.

When applying Batch Normalization with mini-batches, we utilize statistics (mean and variance) derived from the data within each batch. The variability in the data introduces some noise into the normalization, which may lead to minor information loss.

The selected batch size can impact the extent of this noise. Generally, larger batches can mitigate noise but also demand more memory and extend training duration. Thus, utilizing mini-batches strikes a balance to make the training process manageable. If we were to avoid mini-batches, we would need to handle the entire dataset in one go.

Let's look at an example!

In the following image, we illustrate calculations performed for a specific position within the original batch:

This results in a newly normalized batch that retains the same size but has a different distribution.

Beyond mere computational feasibility, mini-batches offer additional advantages:

• The noise introduced by mini-batch statistics can function as a form of regularization. It introduces a degree of randomness into training, helping to prevent overfitting.
• Each mini-batch represents a unique data subset, causing the normalization statistics to differ slightly with each batch. This variability aids the model in adapting to changes in data distribution throughout the training process.

How Mini-Batches Affect CNN Outputs

In the initial article of this series, we identified three primary types of convolutions: (1) spatial convolutions, (2) depthwise convolutions, and (3) pointwise convolutions.

Spatial convolutions encompass the concepts we've previously covered. In depthwise convolutions, a single convolutional filter is applied independently to each channel, followed by a pointwise convolution (1x1) that merges the filtered outputs from the depthwise convolutions.

Batch Normalization is typically implemented after depthwise and pointwise convolutions and is applied on a channel-wise basis, meaning that each channel is normalized separately.

This channel-wise application of Batch Normalization enhances training stability and allows for tailored normalization benefits for each channel. As a result, the model learns more effectively and avoids excessive sensitivity to variations in individual channels.

In conclusion, while mini-batch normalization introduces some noise and potential information loss, the advantages of improved generalization, regularization, and computational efficiency render it an invaluable technique in contemporary Deep Learning.

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