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LION: A Clifford Neural Paradigm for Multimodal-Attributed Graph Learning

Xunkai Li, Zhengyu Wu, Zekai Chen, Henan Sun, Daohan Su, Guang Zeng, Hongchao Qin, Rong-Hua Li, Guoren Wang

TL;DR

LION tackles the challenge of learning from multimodal-attributed graphs by unifying topology priors with multimodal semantics through a Clifford algebra-based manifold. It introduces CGP to perform alignment via curvature-aware, high-order propagation and AHA to fuse aligned tokens using energy- and scale-aware holographic aggregation, all within a decoupled propagation-then-aggregation framework. The authors provide theoretical guarantees (geometric stability, Dirichlet-energy minimization, and holographic reconstruction bounds) and demonstrate state-of-the-art results across 9 MAG datasets for both graph-centric and modality-centric tasks. The approach yields robust performance with scalable complexity, thanks to a training-free preprocessing phase and a streamlined fusion stage. Overall, LION offers a principled, efficient path to simultaneous modality alignment and fusion on MAGs with practical impact for diverse downstream tasks.

Abstract

Recently, the rapid advancement of multimodal domains has driven a data-centric paradigm shift in graph ML, transitioning from text-attributed to multimodal-attributed graphs. This advancement significantly enhances data representation and expands the scope of graph downstream tasks, such as modality-oriented tasks, thereby improving the practical utility of graph ML. Despite its promise, limitations exist in the current neural paradigms: (1) Neglect Context in Modality Alignment: Most existing methods adopt topology-constrained or modality-specific operators as tokenizers. These aligners inevitably neglect graph context and inhibit modality interaction, resulting in suboptimal alignment. (2) Lack of Adaptation in Modality Fusion: Most existing methods are simple adaptations for 2-modality graphs and fail to adequately exploit aligned tokens equipped with topology priors during fusion, leading to poor generalizability and performance degradation. To address the above issues, we propose LION (c\underline{LI}ff\underline{O}rd \underline{N}eural paradigm) based on the Clifford algebra and decoupled graph neural paradigm (i.e., propagation-then-aggregation) to implement alignment-then-fusion in multimodal-attributed graphs. Specifically, we first construct a modality-aware geometric manifold grounded in Clifford algebra. This geometric-induced high-order graph propagation efficiently achieves modality interaction, facilitating modality alignment. Then, based on the geometric grade properties of aligned tokens, we propose adaptive holographic aggregation. This module integrates the energy and scale of geometric grades with learnable parameters to improve modality fusion. Extensive experiments on 9 datasets demonstrate that LION significantly outperforms SOTA baselines across 3 graph and 3 modality downstream tasks.

LION: A Clifford Neural Paradigm for Multimodal-Attributed Graph Learning

TL;DR

LION tackles the challenge of learning from multimodal-attributed graphs by unifying topology priors with multimodal semantics through a Clifford algebra-based manifold. It introduces CGP to perform alignment via curvature-aware, high-order propagation and AHA to fuse aligned tokens using energy- and scale-aware holographic aggregation, all within a decoupled propagation-then-aggregation framework. The authors provide theoretical guarantees (geometric stability, Dirichlet-energy minimization, and holographic reconstruction bounds) and demonstrate state-of-the-art results across 9 MAG datasets for both graph-centric and modality-centric tasks. The approach yields robust performance with scalable complexity, thanks to a training-free preprocessing phase and a streamlined fusion stage. Overall, LION offers a principled, efficient path to simultaneous modality alignment and fusion on MAGs with practical impact for diverse downstream tasks.

Abstract

Recently, the rapid advancement of multimodal domains has driven a data-centric paradigm shift in graph ML, transitioning from text-attributed to multimodal-attributed graphs. This advancement significantly enhances data representation and expands the scope of graph downstream tasks, such as modality-oriented tasks, thereby improving the practical utility of graph ML. Despite its promise, limitations exist in the current neural paradigms: (1) Neglect Context in Modality Alignment: Most existing methods adopt topology-constrained or modality-specific operators as tokenizers. These aligners inevitably neglect graph context and inhibit modality interaction, resulting in suboptimal alignment. (2) Lack of Adaptation in Modality Fusion: Most existing methods are simple adaptations for 2-modality graphs and fail to adequately exploit aligned tokens equipped with topology priors during fusion, leading to poor generalizability and performance degradation. To address the above issues, we propose LION (c\underline{LI}ff\underline{O}rd \underline{N}eural paradigm) based on the Clifford algebra and decoupled graph neural paradigm (i.e., propagation-then-aggregation) to implement alignment-then-fusion in multimodal-attributed graphs. Specifically, we first construct a modality-aware geometric manifold grounded in Clifford algebra. This geometric-induced high-order graph propagation efficiently achieves modality interaction, facilitating modality alignment. Then, based on the geometric grade properties of aligned tokens, we propose adaptive holographic aggregation. This module integrates the energy and scale of geometric grades with learnable parameters to improve modality fusion. Extensive experiments on 9 datasets demonstrate that LION significantly outperforms SOTA baselines across 3 graph and 3 modality downstream tasks.
Paper Structure (25 sections, 5 theorems, 37 equations, 6 figures, 5 tables, 1 algorithm)

This paper contains 25 sections, 5 theorems, 37 equations, 6 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations and Problem Formulation
  4. MAG Neural Paradigm
  5. Methodology
  6. Clifford Algebra and Geometric Manifold
  7. Clifford Geometric Propagation
  8. Adaptive Holographic Aggregation
  9. Experiments
  10. Experimental Setup
  11. Performance Comparison
  12. Ablation Study
  13. In-depth Analysis
  14. Robustness Analysis
  15. Running Efficiency
  16. ...and 10 more sections

Key Result

Theorem 3.1

(Stability Bound of Clifford Manifold). Let $f$ be the mapping function that obtains $\!\mathbf{H}$ and $\mathcal{A_G}\!\coloneqq\!\{\Phi,\mathcal{R}\}$ in the Clifford geometric manifold. Assuming the constituent operations satisfy Lipschitz continuity, for any paired input $(\mathbf{X},\mathbf{A}) where $K_{\text{map}}$ and $\gamma$ are the Lipschitz constant determined strictly by the mathemati

Figures (6)

  • Figure 1: Empirical evaluations of CGP (a) and AHA (b), where the x-axis for AHA (b) is training time in seconds.
  • Figure 2: (a)-(d) The G2Text visualization of CGP modality interaction and alignment (i.e., geometric-induced adaptive graph propagation) on Flickr30k. (e)-(h) The G2Image visualization of CGP modality interaction and alignment on SemArt.
  • Figure 3: Hyperparameter analysis of CGP depth.
  • Figure 4: AHA visualization. T and I are text and image.
  • Figure 5: The model performance of LION on the sparsity Grocery.
  • ...and 1 more figures

Theorems & Definitions (8)

  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • proof
  • Lemma 1.1
  • Lemma 1.2
  • proof
  • proof