Two-dimensional convolutions

In mathematics, we write convolutions as follows:

What this means is that we have a function, f, which is our input and a function, g, which is our kernel. By convolving them, we receive an output (sometimes referred to as a feature map). 

However, in CNNs, we usually use discrete convolutions, which are written as follows:

Let's suppose we have a two-dimensional array with a height of 5 and a width of 5, and a two-dimensional kernel with a height of 3 and a width of 3. Then, the convolution and its output will ...

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