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Discrete Convolution

Slides a filter over an input to detect local patterns; the core of CNNs.

Formula

(fg)(t)=τf(τ)g(tτ)(f*g)(t)=\sum_{\tau} f(\tau)\,g(t-\tau)

Variables

fInput signal
gKernel/filter
\tauShift index

Example

A 3x3 edge kernel highlights boundaries

Did You Know?

Convolutional nets are inspired by the visual cortex, where neurons respond to local regions.

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