24c523085d10743633f9964e0623dbe0-Supplemental-Conference.pdf

We show that there are monotone data sets that cannot be interpolated by a monotone network of depth 2. On the other hand, we prove that for every monotone data set with n points in Rd, there exists an interpolating monotone network of depth 4 and size O(nd). Our interpolation result implies that every monotone function over [0,1]d can be approximated arbitrarily well by a depth4 monotone network, improving the previous best-known construction of depth d+1.