# Collaboration of Fusion and Independence: Hypercomplex-driven Robust Multi-Modal Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2509.23714 · HTML: https://mlsanity.com/paper/2509.23714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (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)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [MMKG: Multi-Modal Knowledge Graphs](https://mlsanity.com/paper/1903.05485/) (2019)
- [Image-embodied Knowledge Representation Learning](https://mlsanity.com/paper/1609.07028/) (2016)
- [Knowledge Graphs Meet Multi-Modal Learning: A Comprehensive Survey](https://mlsanity.com/paper/2402.05391/) (2024)
- [IMF: Interactive Multimodal Fusion Model for Link Prediction](https://mlsanity.com/paper/2303.10816/) (2023)
- [Rethinking Uncertainly Missing and Ambiguous Visual Modality in Multi-Modal Entity Alignment](https://mlsanity.com/paper/2307.16210/) (2023)
- [BiQUE: Biquaternionic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/2109.14401/) (2021)
- [Knowledge Graph Completion with Pre-trained Multimodal Transformer and Twins Negative Sampling](https://mlsanity.com/paper/2209.07084/) (2022)
- [Tele-Knowledge Pre-training for Fault Analysis](https://mlsanity.com/paper/2210.11298/) (2022)
- [Tokenization, Fusion, and Augmentation: Towards Fine-grained Multi-modal Entity Representation](https://mlsanity.com/paper/2404.09468/) (2024)
- [Multiple Heads are Better than One: Mixture of Modality Knowledge Experts for Entity Representation Learning](https://mlsanity.com/paper/2405.16869/) (2024)
- [Learning Representations of Bi-level Knowledge Graphs for Reasoning beyond Link Prediction](https://mlsanity.com/paper/2302.02601/) (2023)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)

## Abstract (arXiv)

Multi-modal knowledge graph completion (MMKGC) aims to discover missing facts in multi-modal knowledge graphs (MMKGs) by leveraging both structural relationships and diverse modality information of entities. Existing MMKGC methods follow two multi-modal paradigms: fusion-based and ensemble-based. Fusion-based methods employ fixed fusion strategies, which inevitably leads to the loss of modality-specific information and a lack of flexibility to adapt to varying modality relevance across contexts. In contrast, ensemble-based methods retain modality independence through dedicated sub-models but struggle to capture the nuanced, context-dependent semantic interplay between modalities. To overcome these dual limitations, we propose a novel MMKGC method M-Hyper, which achieves the coexistence and collaboration of fused and independent modality representations. Our method integrates the strengths of both paradigms, enabling effective cross-modal interactions while maintaining modality-specific information. Inspired by ``quaternion'' algebra, we utilize its four orthogonal bases to represent multiple independent modalities and employ the Hamilton product to efficiently model pair-wise interactions among them. Specifically, we introduce a Fine-grained Entity Representation Factorization (FERF) module and a Robust Relation-aware Modality Fusion (R2MF) module to obtain robust representations for three independent modalities and one fused modality. The resulting four modality representations are then mapped to the four orthogonal bases of a biquaternion (a hypercomplex extension of quaternion) for comprehensive modality interaction. Extensive experiments indicate its state-of-the-art performance, robustness, and computational efficiency.