This paper proposes an unautoregressive framework for the traveling salesman problem (TSP). This framework derives solutions directly from learned permutations without explicit exploration. By applying similar transformations to Hamiltonian cycles, the model learns to approximate the permutation matrix through successive relaxations. This unsupervised learning approach achieves performance comparable to conventional heuristic algorithms, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without requiring sequential decision-making. This study provides concrete evidence that neural networks can directly capture and utilize combinatorial structure.
