It’s simple, they do not. A network, convoluted or otherwise is incapable of learning. Only of a (mostly) whole human being and some non human animals with a (mostly) fully functioning nervous system including a brain, can we say it is capable of learning. Much like a brain, except not at all like it in any way, a neural network cannot learn. It does not matter if that neural network is in a human brain or a computer. It is also important to realize that a neural network is still only a hypothesized structure/functional component of the human brain. There may actually not be such networks, or if there are they may function in totally different ways from how they are theorized to today. If it turns out neural networks in the brain do no exist, or we are completely wrong about their structure/function what does that say about artificial neural networks which are “modeled” after them? Math with weights is not learning. It is math. Just because the math can be adjusted over times based on input values doesn’t make it magical learning math, it makes it math. The computers/machines doing this math (aka computing, thus the name), are doing what they always have done, and always will do, calculating and outputting data based on input data and their programming. What they are not doing, and logically cannot ever do, is learning/learn. They are incapable of doing so and if one ever did develop/was given/emerged the capability to learn it would no longer be a machine. I do love the name though, convolutional neural network sounds awfully important and smart. You know what would make it seem even more important/significant and just plain cooler, putting the word deep in front of it. Deep convolutional neural networks. Now that’s good stuff. That kind of magic will get your machine learning in no time flat.