A general approximation lower bound in L p norm, with applications to feed-forward neural networks Supplementary Material

This is the appendix for "A general approximation lower bound in We provide technical details that were missing to establish Proposition 1, Theorem 1 and Corollary 1. A node u V is a predecessor of another node v V if there is a directed edge from u to v . Note that every g G is indeed [0, 1] -valued. Before proving the two properties (see below), we first conclude the proof of Proposition 1. We now prove the two properties. Proof of Property 2. Let The reverse inequality is proved similarly.B.2 Clipping can only help The next two lemmas indicate that clipping (truncature) to a known range can only help. Note that (16) implies that f (1 /ε) cP . This bound was refined for piecewise-affine activation functions.