Analog versus discrete neural networks.
We show that neural networks with three-times continuously differentiable activation functions are capable of computing a certain family of n-bit boolean functions with two gates, whereas networks composed of binary threshold functions require at least omega(log n) gates. Thus, for a large class of activation functions, analog neural networks can be more powerful than discrete neural networks, even when computing Boolean functions.
DasGupta
B
B
Department of Computer Science, University of Waterloo, Ontario, Canada.
Schnitger
G
G
D003202:Computers, Analog; D008433:Mathematics; D016571:Neural Networks, Computer; D009474:Neurons