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

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.

💡 Research Summary

The paper introduces LION, a novel neural paradigm for multimodal-attributed graphs (MAGs) that leverages Clifford algebra to create a modality‑aware geometric manifold. The authors first identify two major shortcomings in existing MAG neural networks: (1) alignment methods ignore the broader graph context, limiting modality interaction, and (2) fusion mechanisms are either naïve or designed only for two modalities, failing to exploit the rich topology‑aware tokens produced after alignment.

To overcome these issues, LION adopts a decoupled propagation‑then‑aggregation framework. In the propagation stage, called Clifford Geometric Propagation (CGP), each node’s multimodal features are lifted into a 2K‑dimensional space spanned by the Clifford algebra Cl_K, where each modality corresponds to an orthogonal Grade‑1 basis vector. This construction yields a hierarchy of geometric grades: Grade‑0 (scalar) captures intra‑modality similarity, Grade‑2 (bivector) encodes pairwise modality interactions, and higher grades (for K ≥ 3) model multi‑way interactions.

CGP defines two key operators derived from the manifold’s curvature: a spatial rotor R_uv and a geometric potential Φ_uv. R_uv is a rotation matrix computed from the bivector norm of the inner product between neighboring node embeddings, effectively “parallel‑transporting” modality bases along the graph’s curvature. Φ_uv combines scalar and bivector norms in an exponential decay kernel, providing a normalized weight that reflects both intra‑ and inter‑modality similarity. Importantly, CGP is training‑free; it performs a single high‑order propagation step without learnable parameters, yet it respects the manifold’s geometry and preserves signal energy. Theoretical contributions include a Lipschitz‑based stability bound (Theorem 3.1) and a proof that CGP minimizes a Clifford‑Dirichlet energy, guaranteeing that the propagation aligns modalities in a principled manner.

After alignment, the Adaptive Holographic Aggregation (AHA) module fuses the aligned tokens. AHA exploits the geometric grade properties of the propagated embeddings: each grade’s energy (inner‑product magnitude) and scale (norm) are multiplied by learnable scalar coefficients, forming a dynamic filter that emphasizes the most informative topological and modal cues while suppressing noise. This grade‑aware aggregation goes beyond simple concatenation or fixed‑attention schemes, allowing the model to adaptively balance contributions from different modalities and graph structures.

Empirically, LION is evaluated on nine datasets spanning three domains (text, image, video) and six downstream tasks: three graph‑centric tasks (node classification, link prediction, node clustering) and three modality‑centric tasks (cross‑modal retrieval, text generation, image generation). Across all benchmarks, LION outperforms state‑of‑the‑art baselines by an average of 5.24 % on graph tasks and 7.68 % on modality tasks. Ablation studies show that replacing existing alignment modules with CGP consistently improves performance, confirming its plug‑and‑play nature. Moreover, the full LION (CGP + AHA) converges faster and achieves higher final scores than variants lacking AHA, highlighting the importance of grade‑aware fusion.

In summary, LION presents a mathematically grounded solution to multimodal graph learning by unifying topology and modality within a Clifford‑algebraic manifold, providing a parameter‑free, curvature‑driven alignment mechanism, and a learnable, grade‑sensitive aggregation. This work opens a new direction for graph neural networks that can natively handle rich multimodal information while preserving the expressive power of high‑order geometric reasoning.