Reviews: Exponential expressivity in deep neural networks through transient chaos

This is a very interesting work. However, I have a few major concerns: 1) I believe Theorem 1 is wrong, as can be seen from the counterexample at the bottom of this review. As can be observed from this counterexample, the main problem in the proof is the inaccurate sentence on lines 110-112 in the supplementary material. I'll wait to author's feedback before deciding if this a fatal flaw. In this case, h_i l are all composed of different linear sums of the same random vector x {l-1}, and are therefore dependent.