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

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.