Discrete convolution

Deep learning · Formula · Appears in 1 lesson

(f∗g)[n]=∑mf[m] g[n−m](f * g)[n] = \sum_{m} f[m]\, g[n-m]

Slides one signal over another, multiplying and summing at every offset. Reusing the same small kernel everywhere is what gives convolutional networks translation equivariance and their very small parameter count.

Symbols

ff
The input signal, such as an image row.
gg
The kernel being slid across it.
nn
The output position.
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