Before revision:  Moreover, we bound the size of the neural network needed to represent each iterate in terms of the neural network representing the previous iterate, resulting in a final network whose parameters depend polynomially on d and does not depend on the volume of the domain.
After revision:  Moreover, we bound the size of the neural network needed to represent each iterate in terms of the neural network representing the previous iterate, resulting in a final network whose parameters depend polynomially on d and no dependence on the volume of the domain.