Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization
This addresses combinatorial optimization for researchers by showing neural networks can capture structure without sequential decision-making, though it appears incremental as it builds on existing unsupervised and permutation-based methods.
The paper tackles the Travelling Salesman Problem by proposing a non-autoregressive framework that learns permutations directly without explicit search, achieving competitive performance against classical heuristics.
We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the model learns to approximate permutation matrices via continuous relaxations. Our unsupervised approach achieves competitive performance against classical heuristics, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without sequential decision-making. Our method offers concrete evidence that neural networks can directly capture and exploit combinatorial structure.