Convolutional Neural Networks

A Convolutional Neural Network (CNN) is a specialized type of neural network designed to process grid-like data, most commonly images. Instead of treating every pixel as an independent input like a standard MLP, CNNs preserve and exploit the spatial structure of the data.

The Convolution Operation

A CNN slides a small matrix called a filter (or kernel) across the input image, computing a dot product at each position. This produces a feature map that highlights where a particular pattern - like an edge, curve or texture - appears in the image.

output_pixel = sum(filter * image_patch)

Why Not Just Use an MLP?

A standard MLP would need a separate weight for every single pixel connection, making it computationally massive and prone to overfitting for images. CNNs solve this through parameter sharing (the same filter is reused across the entire image) and local connectivity (each neuron only looks at a small region at a time).

Typical CNN Architecture

Input Image -> Convolution + Activation -> Pooling -> Convolution + Activation -> Pooling -> Fully Connected -> Output

Implementing in Python

from tensorflow.keras import layers, models

model = models.Sequential([
    layers.Conv2D(32, (3,3), activation="relu", input_shape=(64,64,3)),
    layers.MaxPooling2D((2,2)),
    layers.Flatten(),
    layers.Dense(10, activation="softmax")
])

Early layers in a CNN tend to learn simple patterns like edges and colors, while deeper layers combine these into increasingly complex features like shapes, textures and eventually whole objects.

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