I think its worth pointing out that when computer science researchers play with different kinds of neural nets which expand beyond the simplistic version used in the OP, they still call them neural nets. I have seen abstract computer-driven neural nets that fire independently and in (more) continuous time, are plastic, lack clear layers, etc.
I think when you said: "but I'm talking about a neural net as a specific mathematical model here" that is fair, you are asserting that while this model similar to a biological one at some very primitive level the model of neural net used here is so far removed for our biological implementation as to render any comparison non-meaningful. I believe that is possible, but we still have discussed evidence that is the case.
I thought it might not be "silly" question: Consider that a turning machine simulated with pencil and paper, given enough paper and time is capable of doing any calculation your desktop computer can. Now it may take 10,000+ years and many "operators" lives, but that is besides the point.
I was thinking that the comparison between the pencil and paper turning machine and the desktop machine, might be similar to the this very basic neural net model and our own much more complex biological instance. The idea is that the two systems while varying vastly in efficiency might equivalent in what they can theoretically compute.
I don't see how asking the question of how much we can simplify our biological neural net and still have be computationally equivalent to the original (even if less efficient) is a silly question.
(I don't like silly, it implies the question is not worth asking. Calling your students question silly is a good way to make them never ask another.)
I think its worth pointing out that when computer science researchers play with different kinds of neural nets which expand beyond the simplistic version used in the OP, they still call them neural nets. I have seen abstract computer-driven neural nets that fire independently and in (more) continuous time, are plastic, lack clear layers, etc.
I think when you said: "but I'm talking about a neural net as a specific mathematical model here" that is fair, you are asserting that while this model similar to a biological one at some very primitive level the model of neural net used here is so far removed for our biological implementation as to render any comparison non-meaningful. I believe that is possible, but we still have discussed evidence that is the case.
I thought it might not be "silly" question: Consider that a turning machine simulated with pencil and paper, given enough paper and time is capable of doing any calculation your desktop computer can. Now it may take 10,000+ years and many "operators" lives, but that is besides the point.
I was thinking that the comparison between the pencil and paper turning machine and the desktop machine, might be similar to the this very basic neural net model and our own much more complex biological instance. The idea is that the two systems while varying vastly in efficiency might equivalent in what they can theoretically compute.
I don't see how asking the question of how much we can simplify our biological neural net and still have be computationally equivalent to the original (even if less efficient) is a silly question.
(I don't like silly, it implies the question is not worth asking. Calling your students question silly is a good way to make them never ask another.)