# 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

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

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 $$n \times n$$.