  We provide a comprehensive reply to the comment written by Chiara Angelini
and Federico Ricci-Tersenghi [arXiv:2206.13211] and argue that the comment
singles out one particular non-representative example problem, entirely
focusing on the maximum independent set (MIS) on sparse graphs, for which
greedy algorithms are expected to perform well. Conversely, we highlight the
broader algorithmic development underlying our original work, and (within our
original framework) provide additional numerical results showing sizable
improvements over our original results, thereby refuting the comment's
performance statements. We also provide results showing run-time scaling
superior to the results provided by Angelini and Ricci-Tersenghi. Furthermore,
we show that the proposed set of random d-regular graphs does not provide a
universal set of benchmark instances, nor do greedy heuristics provide a
universal algorithmic baseline. Finally, we argue that the internal (parallel)
anatomy of graph neural networks is very different from the (sequential) nature
of greedy algorithms and emphasize that graph neural networks have demonstrated
their potential for superior scalability compared to existing heuristics such
as parallel tempering. We conclude by discussing the conceptual novelty of our
work and outline some potential extensions.
