Gauge-Invariant Learnable Spectral Positional Encodings for Directed Graphs via Hermitian Block Krylov Subspaces
arXiv:2607.07032v1 Announce Type: new Abstract: Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures. We propose learnable spectral PEs of the form $h_\theta(A_q)\,R$, where $A_q$ is a normalized magnetic operator, $h_\theta$ a learnable scalar spectral response, and $R$ a block of random probes. Because the PE is a \emph{matrix function} of the operator,
The paper addresses a known technical limitation in applying spectral positional encodings to directed graphs within the rapidly evolving field of AI research, particularly in graph neural networks.
Improved methods for handling complex graph structures can enhance the capabilities and efficiency of AI models applied to intricate datasets like social networks, molecular structures, and knowledge graphs.
This research introduces a more efficient and robust way to incorporate positional information in graph neural networks for directed graphs, potentially leading to more accurate and scalable AI applications.
- · AI researchers and developers
- · Companies utilizing graph-based AI
- · Sectors with complex relational data
- · Prior less efficient methods for directed graph PEs
More accurate and scalable graph neural networks are developed for directed graphs.
New AI applications emerge that leverage the enhanced understanding of relational data.
Industries reliant on complex data relationships (e.g., drug discovery, fraud detection) see performance improvements.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG