I wrote “Solving The Travelling Salesmen Problem using HNN and HNN-SA algorithms” (arXiv:2202.13746) in February 2022. The study compares Hopfield neural networks and simulated annealing on TSP instances. The picture is not a figure from that note.
Fig. 1A tangled tour through eleven dots shortens, one swap at a time, into the shortest loop. The tour is computed by a 2-opt search over these eleven points, not by the paper’s Hopfield network. The final loop is the optimal tour for them.