That's a really good question... I know that normal network training is basically "y=mx+b, solve for m and b." But then you add layers and transfer functions,

That's a really good question... I know that normal network training is basically "y=mx+b, solve for m and b." But then you add layers and transfer functions, so it's more like: y1=f(m1y2)+b1 y2=f(m2yn)+b2 ... And then you solve for each mn and bn, using f^(-1), which is why smooth transfer functions are preferred, and then on some networks you can visualize the training space, with the derivative pointing toward the most optimal position. But, a spiking neural network that isn't smooth seems like you wouldn't form clean gradients for training, so that's actually a really good question... Seems like it wouldn't work correctly, or would be incredibly difficult to train. Of course maybe "spiking" is a name for another part of the behavior, and not the transfer function itself.