Review for NeurIPS paper: Semialgebraic Optimization for Lipschitz Constants of ReLU Networks

Weaknesses: First, other works in this area usually show the advantage of the estimated Lipschitz constant on robustness certification tasks or other downstream tasks, empirically or theoretically (see [1], [2], and [3]). Without those experiments and only looking at the upper bounds of the Lipschitz constant of neural networks, it is hard to evaluate the significance of the work. Second, the upper bounds of the Lipschitz constant and the corresponding computational times also do not clearly show the advantage of the proposed method. For example, in table 2, when computing upper bounds of global Lipschitz constant and the solver running time on the trained network, while the proposed method achieves better upper bounds, it requires much more computational time. Again, this further emphasizes the need of additional experiments on downstream tasks such as robustness certification to justify the significance of the method.