Classifying the Graph Topology of Non-Hermitian Energy Spectra with Graph Transformer.
Published in AAAI 2026 XAI4Science Workshop, 2025
Abstract: Classifying non-Hermitian energy spectra under open boundary conditions is an open challenge in physics.
This classification is a critical prerequisite for the rational inverse design of systems exhibiting desired dynamics and topological responses. While graph topology has emerged as a promising approach for characterizing these spectra, systematic methods for distilling non-Hermitian spectra into their corresponding graph representations have been lacking. Moreover, the resulting graphs often exhibit complexities that defy manual classification, necessitating machine learning approaches.
In this work, we introduce a two-step framework for classifying non-Hermitian spectra based on their graph topologies. The first step employs Poly2Graph, an automated, high-performance pipeline that distills non-Hermitian spectra into spectral graphs suitable for graph neural networks (GNNs). The second step involves generating a large dataset of these spectral graphs and training a GNN for classification. We propose GnLTransformer, a novel architecture featuring dual channels that leverage line graphs to explicitly capture higher-order topological features. GnLTransformer achieves over 99% classification accuracy on our dataset, outperforming standard baselines by 32%. Notably, beyond conventional GNNs, GnLTransformer offers inherent explainability regarding higher-order topology. As a further contribution, we release a new multi-graph dataset comprising over 117K spectral graphs.