Geometric Structural Knowledge Graph Foundation Model
Ling Xin, Mojtaba Nayyeri, Zahra Makki Nayeri, Steffen Staab

TL;DR
Gamma introduces multi-head geometric attention with diverse algebraic transformations for knowledge graph reasoning, significantly improving zero-shot inductive link prediction across diverse graphs.
Contribution
It proposes Gamma, a foundation model with multi-space relational transformations and adaptive fusion, enhancing expressiveness over existing single-space approaches.
Findings
Outperforms Ultra with 5.5% MRR improvement on inductive benchmarks.
Demonstrates consistent 4.4% overall performance boost.
Effectively models diverse relational structures with multiple algebraic spaces.
Abstract
Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation (e.g., element-wise multiplication) in message passing, which can constrain expressiveness and fail to capture diverse relational and structural patterns exhibited on diverse graphs. In this paper, we propose Gamma, a novel foundation model that introduces multi-head geometric attention to knowledge graph reasoning. Gamma replaces the single relational transformation with multiple parallel ones, including real, complex, split-complex, and dual number based transformations, each designed to model different relational structures. A relational conditioned attention fusion mechanism then adaptively fuses them at link level via a lightweight gating with…
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Taxonomy
TopicsAdvanced Graph Neural Networks · Graph Theory and Algorithms · Data Visualization and Analytics
