Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles

• URL: http://arxiv.org/abs/2606.03270v1
• Date: Tue, 02 Jun 2026 07:35:42 GMT
• Title: Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
• Abstract summary: We develop a graph intrinsic geometry learning framework called Neural Vector Bundle.<n>Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle and flattens geometrically compatible local coordinates.<n>We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.
• Score: 53.65187206795911
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework called Neural Vector Bundle, which enables parsing intrinsic geometry with local coordinates. Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.

Related papers

• Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence [51.30336200738606]
  There is strong agreement that Graph Foundation Models (GFMs) are essential for advancing graph learning.<n> considerable disagreement persists on how to build a powerful, general-purpose GFM analogous to Large Language Models (LLMs)
  arXiv  Detail & Related papers  (2026-03-23T05:49:19Z)
• Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models [43.64910777659052]
  Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains.<n>Existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains.<n>We present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence.
  arXiv  Detail & Related papers  (2026-02-28T12:22:19Z)
• GraphShaper: Geometry-aware Alignment for Improving Transfer Learning in Text-Attributed Graphs [16.624063216788638]
  We introduce textbfGraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization.<n>Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties.<n>It achieves 9.47% accuracy improvements on citation networks and 7.63% on social networks in zero-shot settings.
  arXiv  Detail & Related papers  (2025-10-14T02:48:50Z)
• Learning the Structure of Connection Graphs [13.687470962704744]
  Connection graphs (CGs) extend traditional graph models by coupling network topology with transformations, enabling the representation of global geometric consistency.<n>We propose a principled framework based on maximum pseudo-likelihood under a consistency assumption, which enforces spectral properties linking the connection Laplacian to the underlying Laplacian.<n>We introduce the Structured Connection Graph Learning (SCGL) algorithm, a block-optimization procedure that jointly infers network topology, edge weights, and geometric structure.
  arXiv  Detail & Related papers  (2025-10-13T10:33:31Z)
• Adaptive Riemannian Graph Neural Networks [29.859977834688625]
  We introduce a novel framework that learns a continuous and anisotropic metric tensor field over the graph.<n>It allows each node to determine its optimal local geometry, enabling the model to fluidly adapt to the graph's structural landscape.<n>Our method demonstrates superior performance on both homophilic and heterophilic benchmark geometries.
  arXiv  Detail & Related papers  (2025-08-04T16:55:02Z)
• Why Neural Network Can Discover Symbolic Structures with Gradient-based Training: An Algebraic and Geometric Foundation for Neurosymbolic Reasoning [73.18052192964349]
  We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics.<n>By lifting neural parameters to a measure space and modeling training as Wasserstein gradient flow, we show that under geometric constraints, the parameter measure $mu_t$ undergoes two concurrent phenomena.
  arXiv  Detail & Related papers  (2025-06-26T22:40:30Z)
• RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry [19.299795173943476]
  Graph neural networks excel at learning graph data, the omnipresent non-Euclidean structure, but often lack the generalization capacity.<n>Recent efforts have been made to leverage Large Language Models.<n>Key innovation is the discovery of a simple yet effective structural vocabulary of trees and cycles.
  arXiv  Detail & Related papers  (2025-02-05T15:06:09Z)
• Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning [77.1421343649344]
  We propose a generalization of Transformers towards operating entirely on the product of constant curvature spaces. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges.
  arXiv  Detail & Related papers  (2023-09-08T02:44:37Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Geometrically Principled Connections in Graph Neural Networks [66.51286736506658]
  We argue geometry should remain the primary driving force behind innovation in the emerging field of geometric deep learning. We relate graph neural networks to widely successful computer graphics and data approximation models: radial basis functions (RBFs) We introduce affine skip connections, a novel building block formed by combining a fully connected layer with any graph convolution operator.
  arXiv  Detail & Related papers  (2020-04-06T13:25:46Z)

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.