Just get the sum once, once we have the summed matrix or the dot product, we can get the non-linear function activated on the sum and move forward with the network. This is about the forward pass.
http://ufldl.stanford.edu/tutorial/supervised/ConvolutionalNeuralNetwork/
http://docs.gimp.org/en/plug-in-convmatrix.html
http://andrew.gibiansky.com/blog/machine-learning/convolutional-neural-networks/
cloudmicrophysics 