02.01 · Convolutional Neural Networks

Level: Intermediate
Pre-reading: 02 · Deep Learning Overview

What is a CNN?

A Convolutional Neural Network (CNN) is designed for spatial data like images. Instead of fully connecting every neuron, CNNs use convolutions — sliding filters that detect local patterns.

graph LR A["Image<br/>28×28 pixels"] --> B["Conv Layer 1<br/>32 filters"] B --> C["Pool Layer<br/>Downsample"] C --> D["Conv Layer 2<br/>64 filters"] D --> E["Pool Layer"] E --> F["Flatten<br/>to vector"] F --> G["Dense Layers<br/>Classification"]

Convolution Operation

A convolution slides a learnable filter (kernel) over the input and computes element-wise products and sums.

Filter detects patterns like: - Horizontal edges - Vertical edges - Corners - Textures - Shapes

Input:        Filter:       Output:
1 2 3         1 0 -1        (1+2-3)+... = result
4 5 6         2 0 -2
7 8 9         1 0 -1

Key CNN Components

Component Role
Convolution Apply filters, detect patterns
Pooling Downsample, reduce spatial dimensions
Activation ReLU, add non-linearity
Flatten Convert 2D feature maps to 1D
Dense Fully connected layers for classification

Why CNNs Work for Images

  • Local connectivity: Neurons only connect to local patches (more efficient than fully connected)
  • Weight sharing: Same filter applied everywhere (fewer parameters)
  • Hierarchy: Early layers detect edges, later layers detect shapes, top layers detect objects
What's the difference between convolution and correlation?

Technically, convolution flips the filter, correlation doesn't. In deep learning, we call it convolution but actually do correlation. It doesn't matter — both work fine.

Why use pooling?

Pooling downsamples the feature maps, reducing parameters and computation. It also makes features more robust to small shifts.