if f is the logistic function, then neural networks basically correspond to logistic regression.

http://en.wikipedia.org/wiki/Logistic_regression

which has been around since the 1940s... (multilayer neural networks correspond to hierarchical logistic regression--just plug them together). this should be in any reasonable stats book.

if you mean mathematically sound in terms of learning, etc, then chris bishops "neural networks and pattern recognition" is pretty good, full of sage advice and justification.