Review for NeurIPS paper: Deep Statistical Solvers

The paper proposes new theoretical results regarding universal approximation property of graph convolutional neural networks and uses and trains them for (approximately) solving optimization problems defined on graphs, in particular arising from a discretization of PDEs. The solver is trained directly from the model energy. The paper was recognized by reviewers as having an interesting contribution and meeting the quality standards. The authors are invited to submit the final version including the rebuttal points, addressing all minor revision issues and the literature connections mentioned. Showing the applicability boundaries by studying failure cases is also highly appreciated.