General response

First of all, we thank the reviewers for their helpful comments and remarks. Moore-Penrose pseudo-inverse which explains why the complexity is only quadratic in K). Adaptative Neural Trees ([2]) and Deep Neural Decision Forests ([3]) are both built from decision trees. It is true that a standard regression tree with enough leaves can also approximate a smooth link function. We'll modify lines 228-230 as In that case, the distribution of x over regions is concentrated on one region.