Convolutional networks (CNNs)

Level AdvancedDifficulty ★★★★★Application⌖ Open in the map

What is it?

Networks whose layers convolve the input with small learned kernels: translation-equivariant, with few parameters. The backbone of computer vision since 2012.

Formulas

(K \star I)[i,j] = \sum_{m,n} K[m,n]\,I[i+m,\,j+n]

The mathematics behind it

Convolution★★★★★fundamental
A conv layer slides learned kernels over the input (strictly, a cross-correlation: the kernel is not flipped).
Fourier transform★★★★★advanced
Large convolutions can be computed by FFT; Fourier neural operators learn directly in frequency space.

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.