# RELAGRAM: Recursive Latent Graph Model for the Capacitated Vehicle Routing Problem

arXiv: https://arxiv.org/abs/2610.15106 · HTML: https://mlsanity.com/paper/2610.15106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 14 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark](https://mlsanity.com/paper/2306.17100/) (2023)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvement](https://mlsanity.com/paper/2403.15180/) (2024)
- [Probabilistic Tiny Recursive Model](https://mlsanity.com/paper/2605.19943/) (2026)

## Abstract (arXiv)

Latent recursion repeatedly processes internal representations through the same neural network. Recent work has shown this approach to be effective on structured reasoning tasks such as Sudoku and maze solving. However, whether latent recursion can support neural routing remains unclear. We introduce RELAGRAM (Recursive Latent Graph Model), a novel approach that brings latent recursion to graph combinatorial optimization. RELAGRAM encodes a capacitated vehicle routing problem (CVRP) instance as edge tokens; a compact transformer recurrently updates the latent representations of these tokens. An output head maps the answer state to an edge heatmap, from which an autoregressive decoder constructs a feasible solution. On CVRP-100 instances, the 0.53M-parameter RELAGRAM achieves gaps to a PyVRP reference of 13.4%, 9.8%, and 8.3% under greedy decoding, eightfold symmetry augmentation, and 256-candidate search, respectively. Trained only on CVRP-100, RELAGRAM generalizes zero-shot to CVRP-500 and CVRP-1000, achieving gaps of 15.6% and 21.7% under 256-candidate search. Together, these results demonstrate that latent recursion is a promising approach to neural routing.