SupplementaryMaterial

This is the appendix for "A general approximation lower bound inLp norm, with applications to feed-forwardneuralnetworks". Layer L consists of a single node: the output neuron. Note that skip connections are allowed, i.e., there can be connections between non-consecutivelayers. We now explain how to derive Proposition 1 (with an arbitrary range[a,b]) as a straightforward consequenceofProposition7. Proof(ofProposition1). In order to apply Proposition 7, we reduce the problem from[a,b] to [0,1] by translating and rescaling every function inG.