Transport, Don't Generate: Deterministic Geometric Flows for Combinatorial Optimization
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914322198822912 |
|---|---|
| author | Friedmann, Benjy Dym, Nadav |
| author_facet | Friedmann, Benjy Dym, Nadav |
| contents | Recent advances in Neural Combinatorial Optimization (NCO) have been dominated by diffusion models that treat the Euclidean Traveling Salesman Problem (TSP) as a stochastic $N \times N$ heatmap generation task. In this paper, we propose CycFlow, a framework that replaces iterative edge denoising with deterministic point transport. CycFlow learns an instance-conditioned vector field that continuously transports input 2D coordinates to a canonical circular arrangement, where the optimal tour is recovered from this $2N$ dimensional representation via angular sorting. By leveraging data-dependent flow matching, we bypass the quadratic bottleneck of edge scoring in favor of linear coordinate dynamics. This paradigm shift accelerates solving speed by up to three orders of magnitude compared to state-of-the-art diffusion baselines, while maintaining competitive optimality gaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transport, Don't Generate: Deterministic Geometric Flows for Combinatorial Optimization Friedmann, Benjy Dym, Nadav Machine Learning Artificial Intelligence 68T07, 90C27 I.2.6; G.2.2 Recent advances in Neural Combinatorial Optimization (NCO) have been dominated by diffusion models that treat the Euclidean Traveling Salesman Problem (TSP) as a stochastic $N \times N$ heatmap generation task. In this paper, we propose CycFlow, a framework that replaces iterative edge denoising with deterministic point transport. CycFlow learns an instance-conditioned vector field that continuously transports input 2D coordinates to a canonical circular arrangement, where the optimal tour is recovered from this $2N$ dimensional representation via angular sorting. By leveraging data-dependent flow matching, we bypass the quadratic bottleneck of edge scoring in favor of linear coordinate dynamics. This paradigm shift accelerates solving speed by up to three orders of magnitude compared to state-of-the-art diffusion baselines, while maintaining competitive optimality gaps. |
| title | Transport, Don't Generate: Deterministic Geometric Flows for Combinatorial Optimization |
| topic | Machine Learning Artificial Intelligence 68T07, 90C27 I.2.6; G.2.2 |
| url | https://arxiv.org/abs/2602.10794 |