Probing Neural TSP Representations for Prescriptive Decision Support

The field of neural combinatorial optimization (NCO) trains neural policies to solve NP-hard problems such as the traveling salesperson problem (TSP). We ask whether, beyond producing good tours, a trained TSP solver learns internal representations that transfer to other optimization-relevant objectives, in the spirit of transfer learning from other domains. We train several attention-based TSP policies, collect their internal activations, and train probes on node/edge embeddings for two NP-hard prescriptive downstream tasks inspired by real-world logistics scenarios: node-removal sensitivity (identifying the most impactful node to remove) and edge-forbid sensitivity (identifying the most critical edge to retain). On a Euclidean TSP100-trained model, probes for both tasks are competitive with existing baselines. Ensembling probe signals with geometric features outperforms the strongest baselines: 65\% top-1 accuracy (vs. 58\% baseline) for the best-node-removal task, and 73\% top-1 accuracy (vs. 67\% baseline) for the worst-edge identification task. To our knowledge, we are the first to study neural TSP solvers as transferable encoders for prescriptive what-if decision-support objectives beyond tour construction. Finally, we show that transfer accuracy increases with solver quality across training and model scale, suggesting that training stronger NCO solvers also yields more useful encoders for downstream objectives. Our code is available at: github.com/ReubenNarad/tsp_prescriptive_probe