Comments on "The unreasonable effectiveness of neural network approximation" [with reply]

This paper discusses the misleading nature of the rate of approximation result reported in the paper by Dingankar (ibid. vol.44, 1999). In reply, Dingankar explains why the original statement of the theorem in that paper is correct as it stands, and clarifies the statements in the original paper. He points out how a proper understanding of the terminology resolves the first objection of the commentator and briefly outlines the directions he is pursuing in a separate research based on the second and the third recommendations.