# Beyond Solving: Prescriptive Probing for Neural Routing Solvers

arXiv: https://arxiv.org/abs/2602.07216 · HTML: https://mlsanity.com/paper/2602.07216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 23 of 23)

- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Matrix Encoding Networks for Neural Combinatorial Optimization](https://mlsanity.com/paper/2106.11113/) (2021)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [Graph Neural Network Guided Local Search for the Traveling Salesperson Problem](https://mlsanity.com/paper/2110.05291/) (2021)
- [Building Production-Ready Probes For Gemini](https://mlsanity.com/paper/2601.11516/) (2026)
- [Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization](https://mlsanity.com/paper/2502.02941/) (2025)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)

## Abstract (arXiv)

Neural combinatorial optimization (NCO) trains fast heuristics for routing problems, but planners often need more than a single solve: they ask which stop to drop, which transition to preserve, or which subset of stops to remove if a route is infeasible. Answering such counterfactual questions by re-solving each candidate is expensive even when the action set is small. We introduce Prescriptive Probing: using the frozen representations of a trained NCO model to rank candidate interventions for what-if decision support. While recent interpretability work descriptively probes what NCO solvers encode, we ask whether those same representations can prescriptively guide intervention choices on real-road routing problems. Where exhaustive labels are available, we train supervised probes from offline re-solve labels; where they are not (e.g., combinatorial action spaces), we train a lightweight reinforcement learning intervention head. Across real-road benchmarks on the Asymmetric Traveling Salesperson Problem and Capacitated Vehicle Routing Problem, probes built on frozen model representations achieve the strongest performance on a majority of intervention tasks and improve over local-repair heuristics on edge-forbiddance and on key node- and multi-node-removal metrics. We further investigate probeability as a property of the routing model itself, varying model quality, the mix of supervised learning and reinforcement learning, and the architecture family. Overall, our results suggest a new use case for NCO solvers: representations learned for route construction can transfer to decision support.