Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach

2025-01-21

AI Summary

Existing magnetically enhanced directed graph neural networks (MagDG) rely on manually tuned hyperparameters (e.g., the complex-phase parameter *q*) for message passing in the complex domain, resulting in inflexible architectures, coarse-grained information propagation, and neglect of node- and edge-level contextual semantics. To address these limitations, we propose an adaptive complex-domain propagation mechanism: (i) a plug-and-play Magnetic Adaptive Propagation (MAP) module compatible with arbitrary MagDG backbones; and (ii) an end-to-end differentiable framework, MAP++, integrating magnetic Laplacian-based complex graph convolution, parameterized adaptive propagation, differentiable edge-weight learning, and node-aware aggregation. Extensive experiments across 12 benchmark datasets demonstrate strong efficiency and scalability. MAP++ achieves state-of-the-art performance across four diverse downstream tasks—including node classification, link prediction, graph classification, and directed graph generation—validating its effectiveness and generalizability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

The $q$-parameterized magnetic Laplacian serves as the foundation of directed graph (digraph) convolution, enabling this kind of digraph neural network (MagDG) to encode node features and structural insights by complex-domain message passing. As a generalization of undirected methods, MagDG shows superior capability in modeling intricate web-scale topology. Despite the great success achieved by existing MagDGs, limitations still exist: (1) Hand-crafted $q$: The performance of MagDGs depends on selecting an appropriate $q$-parameter to construct suitable graph propagation equations in the complex domain. This parameter tuning, driven by downstream tasks, limits model flexibility and significantly increases manual effort. (2) Coarse Message Passing: Most approaches treat all nodes with the same complex-domain propagation and aggregation rules, neglecting their unique digraph contexts. This oversight results in sub-optimal performance. To address the above issues, we propose two key techniques: (1) MAP is crafted to be a plug-and-play complex-domain propagation optimization strategy in the context of digraph learning, enabling seamless integration into any MagDG to improve predictions while enjoying high running efficiency. (2) MAP++ is a new digraph learning framework, further incorporating a learnable mechanism to achieve adaptively edge-wise propagation and node-wise aggregation in the complex domain for better performance. Extensive experiments on 12 datasets demonstrate that MAP enjoys flexibility for it can be incorporated with any MagDG, and scalability as it can deal with web-scale digraphs. MAP++ achieves SOTA predictive performance on 4 different downstream tasks.

Problem

• Parameter Adjustment
• Information Propagation
• Directed Graph Neural Networks

Innovation

• MAP
• MAP++
• MagDG Optimization