Padding

Definition

Padding in Convolutional Neural Networks (CNNs) refers to the process of adding extra pixels around the border of an input image or feature map. This technique is used to control the spatial dimensions of the output feature maps after convolution operations. Padding ensures that the spatial size of the output can be managed, preventing excessive reduction in size through successive convolutions and preserving important edge information.

Key Concepts

• Types of Padding
  • Valid Padding
  • Same Padding
• Purpose of Padding
• Impact on Feature Maps

Detailed Explanation

Types of Padding

• Valid Padding:

  • Definition: No padding is added to the input. The filter only covers valid regions within the image.
  • Impact: The output feature map is smaller than the input. For an input of size ( n \times n ) with a filter of size ( f \times f ) and stride 1, the output size is ((n - f + 1) \times (n - f + 1)).
  • Use Case: When spatial size reduction is desired and edge information is less critical.

• Same Padding:

  • Definition: Padding is added such that the output feature map has the same spatial dimensions as the input.
  • Impact: The amount of padding added is calculated to ensure that the filter fits the input perfectly. For stride 1, the padding size ( p ) is calculated as ( p = \frac{f - 1}{2} ), where ( f ) is the filter size.
  • Use Case: When maintaining the spatial size is important and preserving edge information is critical.

Purpose of Padding

• Preserve Spatial Dimensions: Ensures the output feature map retains the same height and width as the input, especially useful in deep networks where significant size reduction can occur.
• Edge Information: Helps in preserving information at the edges of the image, which would otherwise be lost without padding.
• Control Output Size: Provides flexibility in designing network architectures by controlling the output size of convolution layers.

Impact on Feature Maps

• Valid Padding: Results in smaller feature maps, potentially losing edge information but reducing the computational load.
• Same Padding: Keeps the feature maps the same size as the input, preserving all spatial information and ensuring that the features at the borders are included in the analysis.

Diagrams

• Valid vs. Same Padding: Diagram showing the difference in output size and padding approach for valid and same padding.

Links to Resources

• Deep Learning Book - Convolutional Networks
• Stanford CS231n: Convolutional Neural Networks for Visual Recognition
• Coursera - Convolutional Neural Networks by Andrew Ng
• Khan Academy - Convolution and Padding

Notes and Annotations

Summary of Key Points

• Valid Padding:
  • No additional pixels are added.
  • Output feature map size is reduced.
  • Used when spatial size reduction is acceptable.
• Same Padding:
  • Adds pixels to maintain the same size as the input.
  • Preserves edge information.
  • Used when it is important to keep the spatial dimensions unchanged.

Personal Annotations and Insights

• Using same padding is particularly useful in deeper networks where maintaining spatial dimensions can help in better learning of features across multiple layers.
• Valid padding can be beneficial when the goal is to gradually reduce the size of the feature maps, thus decreasing the computational complexity in later layers.

Backlinks

• Convolutional Layers: Understanding how padding affects the convolution operation and the resulting feature maps.
• CNN Architectures: The role of padding in maintaining or reducing spatial dimensions across different CNN architectures like VGGNet, ResNet, etc.
• Pooling Layers: How padding interacts with pooling operations, especially in maintaining the dimensions of feature maps.