# Geometric Structural Knowledge Graph Foundation Model

arXiv: https://arxiv.org/abs/2512.22931 · HTML: https://mlsanity.com/paper/2512.22931/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Builds on (most cited first, 30 of 39)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)
- [Knowledge Transfer for Out-of-Knowledge-Base Entities: A Graph Neural Network Approach](https://mlsanity.com/paper/1706.05674/) (2017)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [Towards Foundation Models for Knowledge Graph Reasoning](https://mlsanity.com/paper/2310.04562/) (2023)
- [NodePiece: Compositional and Parameter-Efficient Representations of Large Knowledge Graphs](https://mlsanity.com/paper/2106.12144/) (2021)
- [Bringing Light Into the Dark: A Large-scale Evaluation of Knowledge Graph Embedding Models Under a Unified Framework](https://mlsanity.com/paper/2006.13365/) (2020)
- [Commonsense Knowledge Base Completion with Structural and Semantic Context](https://mlsanity.com/paper/1910.02915/) (2019)
- [InGram: Inductive Knowledge Graph Embedding via Relation Graphs](https://mlsanity.com/paper/2305.19987/) (2023)
- [A*Net: A Scalable Path-based Reasoning Approach for Knowledge Graphs](https://mlsanity.com/paper/2206.04798/) (2022)
- [Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representations](https://mlsanity.com/paper/2110.02834/) (2021)
- [Improving Knowledge Graph Embedding Using Simple Constraints](https://mlsanity.com/paper/1805.02408/) (2018)
- [Relational Message Passing for Fully Inductive Knowledge Graph Completion](https://mlsanity.com/paper/2210.03994/) (2022)
- [AdaProp: Learning Adaptive Propagation for Graph Neural Network based Knowledge Graph Reasoning](https://mlsanity.com/paper/2205.15319/) (2022)
- [Dynamic Anticipation and Completion for Multi-Hop Reasoning over Sparse Knowledge Graph](https://mlsanity.com/paper/2010.01899/) (2020)

## Built on by (most cited first, 1 of 1)

- [Reification as a Transferable Vocabulary: Zero-Shot Link Prediction with Vanilla GNNs](https://mlsanity.com/paper/2609.11347/) (2026)

## Abstract (arXiv)

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.