Before revision:  We prove that when a PDE's coefficients are representable by small neural networks, the parameters required to approximate its solution scale polynomially with the input dimension d and are proportional to the parameter counts of the coefficient neural networks.
After revision:  We prove that when a PDE's coefficients are representable by small neural networks, the parameters required to approximate its solution scale polynomially with the input dimension d and proportionally to the parameter counts of the coefficient neural networks.