But isn't the neural network (like the algorithm described in the article) a mathematical concept? It is. It's a family of models that (a) can be expressed com

But isn't the neural network (like the algorithm described in the article) a mathematical concept? It is. It's a family of models that (a) can be expressed compactly using linear algebra and (b) can represent a large class of mathematical functions. (In fact, the family of neural nets can learn all continuous functions.) "Learning" is typically some variety of gradient descent (on the "error surface" defined by the training set) in the space of parameters. Are the computer-based neural networks so closely modeled after biological equivalents that they would inherit such an optimization? In my opinion, no. Biological neural networks are, in fact, a lot more complicated. They have time behavior, changing network topologies, and chemical influences (neurotransmitters) that play a major role. There's still a lot we don't know about them. I disagree with GP's contention. While the biological neural network was an inspiration for this class of mathematical models, and convolutional behavior (in ANNs, a regularization, or mechanism for reducing the dimensionality of the parameter space, sacrificing training-set performance but often improving test-set performance) may be used in our visual cortex, but artificial neural nets are quite different and, mathematically, most varieties are quite simple.