It does at least respectably well against the Concorde TSP solver although (unsurprisingly) doesn't beat it. Note that this also isn't a neural network that just maps a graph to a TSP solution; instead, the neural network function is a heuristic that guides the greedy construction of a solution one vertex at a time.
https://www.cc.gatech.edu/~lsong/papers/arxiv_rl_combopt.pdf
It does at least respectably well against the Concorde TSP solver although (unsurprisingly) doesn't beat it. Note that this also isn't a neural network that just maps a graph to a TSP solution; instead, the neural network function is a heuristic that guides the greedy construction of a solution one vertex at a time.