# ARC: Leveraging Compositional Representations for Cross-Problem Learning on VRPs

arXiv: https://arxiv.org/abs/2512.18633 · HTML: https://mlsanity.com/paper/2512.18633/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 22 of 22)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [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)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Zero-Shot Task Generalization with Multi-Task Deep Reinforcement Learning](https://mlsanity.com/paper/1706.05064/) (2017)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [A Boolean Task Algebra for Reinforcement Learning](https://mlsanity.com/paper/2001.01394/) (2020)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://mlsanity.com/paper/2412.00346/) (2024)
- [Composition-contrastive Learning for Sentence Embeddings](https://mlsanity.com/paper/2307.07380/) (2023)
- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [Plan Arithmetic: Compositional Plan Vectors for Multi-Task Control](https://mlsanity.com/paper/1910.14033/) (2019)

## Abstract (arXiv)

Vehicle Routing Problems (VRPs) with diverse real-world attributes have driven recent interest in cross-problem learning approaches that efficiently generalize across problem variants. We propose ARC (Attribute Representation via Compositional Learning), a cross-problem learning framework that learns disentangled attribute representations by decomposing them into two complementary components: an Intrinsic Attribute Embedding (IAE) for invariant attribute semantics and a Contextual Interaction Embedding (CIE) for attribute-combination effects. This disentanglement is achieved by enforcing analogical consistency in the embedding space to ensure the semantic transformation of adding an attribute (e.g., a length constraint) remains invariant across different problem contexts. This enables our model to reuse invariant semantics across trained variants and construct representations for unseen combinations. ARC achieves state-of-the-art performance across in-distribution, zero-shot generalization, few-shot adaptation, and real-world benchmarks.