SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver

• URL: http://arxiv.org/abs/2605.24484v1
• Date: Sat, 23 May 2026 09:12:42 GMT
• Title: SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver
• Abstract summary: Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems.<n>Existing solvers are typically limited to symmetric settings or degrade in performance when switching to asymmetric settings.<n>We propose a Spatial Pivot-Aligned Coordinate-free Embedding (SPACE) framework that unifies node representation and solution generation across symmetric and asymmetric VRPs.
• Score: 14.268979449819057
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when switching to asymmetric settings due to input inconsistencies or inherent structural differences, substantially limiting their practicality in real-world scenarios that encompass both scenarios. To address this limitation, we define the spatial position of each node based on the relative distances to a specific set of pivots and further propose a Spatial Pivot-Aligned Coordinate-free Embedding (SPACE) framework that unifies node representation and solution generation across symmetric and asymmetric VRPs. Specifically, we construct a bidirectional Frechet representation using a novel furthest pivot sampling strategy to enable invariant node representations across distinct problem settings. Furthermore, we introduce a weight-decomposed adaptive decoding mechanism that decouples geometric perception from problem representations, mitigating the overfitting of constraint decisions to a specific geometry setting. Extensive experiments on 110 VRP variants, comprising 55 symmetric problems and their asymmetric counterparts, demonstrate that SPACE achieves promising zero-shot generalization in both symmetric and asymmetric VRPs.

Related papers

• MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing [15.591644835298213]
  MView is a multi-view framework that internalizes geometric symmetries as a structural inductive bias to achieve indecision across routing problem variants.<n>Our approach introduces a Multi-view Alternating Attention (MAA) mechanism that enables parallel processing over the $D_4$ symmetry group.<n> Experiments on TSP and CVRP benchmarks, as well as real-world TSPLIB instances, demonstrate that MView achieves competitive solution quality and strong zero-shot generalization.
  arXiv  Detail & Related papers  (2026-05-31T08:09:02Z)
• Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration [71.51826063983434]
  Image restoration is an inherently ill posed inverse problem.<n>We use non strict symmetry as a constraint to formulate the restoration inverse problem.<n>We show that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size.
  arXiv  Detail & Related papers  (2026-05-13T16:22:19Z)
• RADAR: Learning to Route with Asymmetry-aware DistAnce Representations [40.851628215658174]
  Recent neural solvers have achieved strong performance on vehicle routing problems (VRPs)<n> RADAR is a scalable neural framework that augments existing neural VRP solvers with the ability to handle asymmetric inputs.
  arXiv  Detail & Related papers  (2026-03-03T08:13:45Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Toward Manifest Relationality in Transformers via Symmetry Reduction [0.0]
  Transformer models contain substantial internal redundancy.<n>Recent approaches address this by explicitly breaking symmetry.<n>We propose a complementary framework based on symmetry reduction.
  arXiv  Detail & Related papers  (2026-02-21T19:43:17Z)
• Symmetry-Aware Graph Metanetwork Autoencoders: Model Merging through Parameter Canonicalization [37.457412158271126]
  We present an autoencoder framework utilizing ScaleGMNs as invariant encoders.<n>We show that our method aligns Implicit Neural Representations (INRs) and Convolutional Neural Networks (CNNs) under both permutation and scaling symmetries.<n>This approach ensures that similar networks naturally converge within the same basin, facilitating model merging and avoiding regions of high loss.
  arXiv  Detail & Related papers  (2025-11-16T13:57:50Z)
• OrthAlign: Orthogonal Subspace Decomposition for Non-Interfering Multi-Objective Alignment [61.02595549125661]
  Large language model (LLM) alignment faces a critical dilemma when addressing multiple human preferences.<n>We present OrthAlign, an innovative approach to resolve gradient-level conflicts in preference alignment.<n>We show that OrthAlign achieves maximum single-preference improvements ranging from 34.61% to 50.89% after multiple-objective alignment.
  arXiv  Detail & Related papers  (2025-09-29T11:16:30Z)
• Axis-level Symmetry Detection with Group-Equivariant Representation [48.813587457507786]
  Recent heatmap-based approaches can localize potential regions of symmetry axes but often lack precision in identifying individual axes.<n>We propose a novel framework for axis-level detection of the two most common symmetry types-reflection and rotation.<n>Our method achieves state-of-the-art performance, outperforming existing approaches.
  arXiv  Detail & Related papers  (2025-08-14T15:26:53Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Relative Representations: Topological and Geometric Perspectives [50.85040046976025]
  Relative representations are an established approach to zero-shot model stitching.<n>We introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations.<n>Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes.
  arXiv  Detail & Related papers  (2024-09-17T08:09:22Z)
• R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection [26.05910177212846]
  Group Equivariant Convolution (GConv) empowers models to explore underlying symmetry in data, improving performance.<n>We introduce a novel Relaxed Rotation-Equivariant GConv (R2GConv) with only a minimal increase of $4n$ parameters compared to GConv.<n>Based on R2GConv, we propose a Relaxed Rotation-Equivariant Network (R2Net) as the backbone and develop a Relaxed Rotation-Equivariant Object Detector (R2Det) for 2D object detection.
  arXiv  Detail & Related papers  (2024-08-21T16:32:03Z)
• Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries [0.0]
  Non-linear independent dual system (NIDS) is a deep learning surrogate model for discretization-independent, continuous representation of PDE solutions. NIDS can be used for prediction over domains with complex, variable geometries and mesh topologies. Test cases include a vehicle problem with complex geometry and data scarcity, enabled by a training method.
  arXiv  Detail & Related papers  (2021-09-14T23:38:41Z)
• Convex Geometry and Duality of Over-parameterized Neural Networks [70.15611146583068]
  We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We show that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set. In higher dimensions, we show that the training problem can be cast as a finite dimensional convex problem with infinitely many constraints.
  arXiv  Detail & Related papers  (2020-02-25T23:05:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.