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Valid convolution

A valid convolution is a type of convolution operation that does not use any padding on the input.

For an \(n \times n\) input matrix and an \(f \times f\) filter, a valid convolution will return an output matrix of dimensions

\[ \left \lfloor \frac{n - f}{s} + 1 \right \rfloor \times \left \lfloor \frac{n - f}{s} + 1 \right \rfloor \]

where \(s\) is the stride length of the convolution.

This is in contrast to a same convolution, which pads the \(n \times n\) input matrix such that the output matrix is also \(n \times n\).