Review for NeurIPS paper: Training Generative Adversarial Networks by Solving Ordinary Differential Equations

Weaknesses: The hypothesis as it stands now is somewhat under-substantiated. Concretely: From a numerical analysis point of view, truncation error order and long-time convergence of the discrete sequence from numerical differencing are separate concepts. RK methods have higher order convergence on fixed time intervals, but its domain of absolute stability is not fundamentally different from that of forward Euler. All explicit methods suffer from limited stability, especially for stiff or conservative systems. Figure 1 shows this effect, but if one takes smaller step sizes the Euler method will converge.