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