Comments on "On hidden nodes in neural nets" by G. Mirchandani and W. Cao

Abstract

A comment on the above-named work (see ibid., vol.36, p.661-4, 1989) by G. Mirchandani and W. Cao is presented. The main contribution of that paper is a proof of a theorem showing that 'the maximum number of separable regions (M) in the input space is a function of both H and input space dimension (d),' where H is the number of hidden nodes or, equivalently, the number of hyperplanes. The commenter argues that this theorem was proven in the mid-nineteenth century by the mathematician Ludwig Schlafli.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>