Introduced on day 36

Convolution (filter, kernel)

A small grid of weights slid over an input; at each position it multiplies the patch under it by the weights and sums, producing one number per position.

In detail

In deep-learning libraries the operation is cross-correlation (the kernel is not flipped), which makes no difference because the weights are learned. Output length per axis is $\lfloor (n + 2p - d(k-1) - 1)/s \rfloor + 1$ for input $n$ , kernel $k$ , padding $p$ , stride $s$ and dilation $d$ . A layer with $f$ filters over $c_{in}$ channels has $f(k^2 c_{in}) + f$ weights in 2-D.