Transcendental functions in backward error propagation

Abstract

Trigonometric transcendental functions such as the sine and cosine functions are shown to be effective as transfer functions in a backpropagation network. Unlike the logistic function, the cosine and sine transfer functions are capable of solving the XOR problem with one processing node. Experiments using the sine and cosine instead of the logistic function show that these function may converge more quickly for certain classes of problems, especially when polynomial correlations are found in training data. Taylor series expansion shows why, for some problems, these functions may give faster convergence than the logistic function. >