Before revision:  Moreover, when approximating convex, piecewise affine functions by width d+1 ReLU nets, we obtain matching upper and lower bounds on the required depth, proving that our construction is essentially optimal.  ]
After revision:  Moreover, when approximating convex, piecewise affine functions by width d+1 ReLU nets, we obtain matching upper and lower bounds on the required depth, proving that our construction is essentially optimal. ]^d by ReLU nets with width d+3.