Generally CNNs are regularized by L1 and L2 norms on the weights. I am wondering what work (if any) has been done on using statistical functions as regularizers on weights or activites. Upon a search of google scholar and IEEE, I have been unable to turn up anything useful.

I want to show you that Deep Convolutional Neural Nets are not nearly as intimidating as they sound. And I'll prove it by showing you an implementation of one that I made in Google Sheets. Copy it (use the File Make a copy option in top left), and you can then play around with it to see how the different levers affect the model's prediction. The rest of the article will be a short intro to understand the high level intuitions behind Convolutional Neural Nets (CNN), and then some recommended resources for further information. Before continuing, I'd like to make a shout out to FastAI.