A same convolution is a type of convolution where the output matrix is of the same dimension as the input matrix.

For a $n\times n$ input matrix $A$ and a $f\times f$ filter matrix $F$, the output of the convolution $A\ast F$ is of dimension $\lfloor \frac{n+2p-f}{s}\rfloor +1\times \lfloor \frac{n+2p-f}{s}\rfloor +1$ where $s$ represents the stride length and $p$ represents the padding.

In a same convolution:

• $s$ is typically set to $1$
• $p$ is set to $\frac{f-1}{2}$
• $f$ is an odd number

The result is that $A$ is padded to be $n+p\times n+p$ and $A\ast F$ becomes $n\times n$ – the same as the original dimensions of $A$.