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In this paper, we demonstrate the application of generalised rational uniform(Chebyshev) approximation in neural networks. In particular, our activationfunctions are one degree rational functions and the loss function is based onthe uniform norm. In this setting, when the coefficients of the rationalactivation function are fixed, the overall optimisation problem of the neuralnetwork forms a generalised rational uniform approximation problem where theweights and the bias of the network are the decision variables. To optimise thedecision variables, we suggest using two prominent methods: the bisectionmethod and the differential correction algorithm.  We perform numerical experiments on classification problems with two classesand report the classification accuracy obtained by the network using thebisection method, differential correction algorithm along with the standardMATLAB toolbox which uses the least square loss function. We show that thechoice of the uniform norm based loss function with rational activationfunction and the bisection method lead to better classification accuracy whenthe training dataset is either very small or if the classes are imbalanced.

Rational activation functions in neural networks with uniform based loss functions and its application in classification