Geometric Structural Knowledge Graph Foundation Model

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 entropy regularization, allowing the model to robustly emphasize the most appropriate relational bias for each triple pattern. We present a full formalization of these algebraic message functions and discuss how their combination increases expressiveness beyond any single space. Comprehensive experiments on 56 diverse knowledge graphs demonstrate that Gamma consistently outperforms Ultra in zero-shot inductive link prediction, with a 5.5% improvement in mean reciprocal rank on the inductive benchmarks and a 4.4% improvement across all benchmarks, highlighting benefits from complementary geometric representations.