The big idea: A convolutional neural network exploits two facts a plain network ignores.
The two facts
- Nearby pixels belong together
- A feature is the same wherever it appears
A cat's ear: A cat's ear is a cat's ear in the top-left or the bottom-right. A CNN learns it once.
Why a plain network struggles on images: Flattening a 200×200 colour image gives 120,000 inputs. Connecting those to even 1,000 hidden units is 120 million weights in the first layer alone.
Worse, flattening destroys the geometry: the network has no idea which pixels were adjacent, so it must learn every feature separately in every position.
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Convolution
A small grid of weights — a filter, typically 3×3 — is slid across the image. At each position it multiplies and sums, producing a feature map showing where that pattern occurs.
Shared weights
The same filter is used at every position. So one edge detector costs 9 weights instead of 9 per location — this is where the enormous saving comes from.
Pooling
Shrink the feature map by keeping only the strongest value in each small block. Fewer numbers to carry forward, and small shifts in position stop mattering.
Stack and repeat
Early layers find edges. The next combine edges into shapes. Later ones combine shapes into objects. The hierarchy is learned, not designed.
| Plain network | CNN | |
|---|---|---|
| Input | Flattened — geometry lost | Keeps the 2D structure |
| Weights in layer 1 | One per pixel per unit — millions | One small filter, reused |
| A feature moved | Must be relearned in the new position | Already recognised — filters are shared |
| What layers learn | No inherent hierarchy | Edges → shapes → objects |
The basic CNN architecture, layer by layer
| Layer | What it does |
|---|---|
| Input layer | The image as a grid of pixel values |
| Convolutional layer | Slides small filters (kernels) across the image to make feature maps |
| Activation function | Applied to each feature map, e.g. ReLU sets negative values to 0, adding non-linearity |
| Pooling layer | Shrinks each map, e.g. keeps the largest value in each 2×2 block |
| Fully connected layer | Every value connected to every node, combining the features found |
| Output layer | One node per class, giving the predicted category |
Design choices and their effect
| Choice | Effect |
|---|---|
| Number of layers | More layers learn more complex features, but need more data and training time |
| Kernel size | A larger kernel sees a bigger area at once; a smaller one catches fine detail |
| Stride | How far the kernel moves each step: a stride of 2 halves the size of the feature map |
| Activation function | Decides how signals pass on; ReLU is common because it trains fast |
| Loss function | Measures how wrong a prediction is; training adjusts the weights to make it smaller |
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Strong at
- Images, video, and anything with local structure
- Also audio spectrograms and some text
- Recognising a feature wherever it appears
Costs
- Needs large labelled datasets
- Training needs accelerators — days on a GPU
- Many hyperparameters to choose
Fails at
- Data with no spatial meaning — a table of unrelated columns
- Explaining itself, exactly like any network
- Objects at angles it never saw during training
Transfer learning is the practical answer: Training a CNN from scratch needs data and hardware most people do not have. In practice you take a network already trained on millions of general images, keep its learned feature detectors, and retrain only the final layer on your own few thousand examples.
Saying this shows you know how CNNs are actually used.
How this is tested — you must explain convolution and shared weights, and say what they buy over a plain network. It comes up two ways:
Paper 1 Section A
- Describe how a CNN learns spatial hierarchies, 4-5 marks
- State what a filter does
- Explain the purpose of pooling
Paper 1 Section B — case study
- Justify a CNN for a scenario
- Explain why a plain network is unsuitable
The classic trap: Describing a CNN as "a neural network for images" and stopping. The marks are for convolution (a small filter slid across), shared weights (the same filter everywhere) and pooling — the three things that make it different.
A hospital wants to detect tumours in X-ray images. Describe how a CNN suits this better than a plain neural network, and state one practical difficulty.
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