Convolutional neural networks (CNNs) are a class of neural networks designed for data with a grid structure, typically images. Their foundation is the convolutional layer: a small filter (kernel), say 3×3 in size, slides across the whole input and at each position computes a weighted sum of the local neighbourhood. Two key properties follow from this. Local connectivity means a neuron sees only a small crop rather than the entire image, which radically reduces the number of parameters. Weight sharing means the same filter is applied at every position, so the network is largely invariant to translation – an edge stays an edge wherever it happens to be. Layers stack into a hierarchy and their receptive field widens with depth: the first layers respond to edges and colour gradients, the middle ones to textures and object parts, the deep ones to whole objects. Pooling layers progressively reduce the resolution. CNNs dominated computer vision from the AlexNet breakthrough in 2012; in many tasks they are now being replaced by vision transformers, though they remain essential in diffusion models and on edge devices.
Imagine you have an enormous photograph and only a tiny peephole the size of a postage stamp. You move the peephole across the whole picture systematically, left to right and top to bottom, noting down one single thing: “vertical edge here, none there”. What emerges is a new, simpler map of edges. Over that map you then run a different peephole, one that looks for corners made of edges. And over that another, which assembles corners into circles, and eventually into a wheel, a wing and a car. You never have to see the whole image at once – and crucially, you recognize an edge just as well in the bottom-left corner as in the middle.