11. Convolutional

Introduction to Convolutional Neural Networks (CNNs)

Convolutional Neural Networks (CNNs) are a class of deep neural networks commonly used for image recognition, video analysis, and other tasks involving grid-like data (e.g., pixels in images). Unlike fully connected networks, CNNs exploit spatial hierarchies through convolutions, which apply learnable filters (kernels) to local regions of the input. This reduces parameters, enables translation invariance, and captures features like edges, textures, or objects.

A typical CNN architecture includes:

• Convolutional layers: Extract features via convolution.
• Activation functions (e.g., ReLU): Introduce non-linearity.
• Pooling layers (e.g., max pooling): Downsample to reduce spatial dimensions and computational load.
• Fully connected layers: For final classification or regression.
• Output layer: Often softmax for classification.

Training involves the forward pass (computing predictions) and backward pass (backpropagation to update weights via gradients). Below, I'll focus on the math for the convolutional layer, as it's the core of CNNs. I'll assume 2D convolution for images (input shape: batch_size × channels × height × width).