Learnable Fractional Fourier and Graph Fractional Operators for Nonstationary Graph Signals Validated with EEG Seizure Detection

ICLR 2026 Conference Submission3686 Authors

Keywords: AI for health.+Graph Fractional Operator.+Epilepsy Detection

TL;DR: Adaptive Fractional Fourier Transform with Graph Functional Connectivity for Epileptic Seizure Detection

Abstract: Nonstationary graph signals with time-varying spectral properties and evolving network topologies present fundamental challenges for existing deep learning architectures. We introduce learnable fractional operators that bridge time-frequency analysis and functional connectivity through trainable fractional orders. We propose EEG-GraphFrFT, a unified dual-path framework implementing this approach. The first path employs a fractional Fourier transform with a trainable order to adaptively capture nonstationary, transient patterns. The second path constructs functional networks derived from wPLI and Spectral Granger causality and applies graph fractional operators to model complex network interactions. We establish the minimal theoretical properties required for stable training, namely well-posedness and Hölder-type stability, under mild spectral assumptions. A parameter-efficient low-rank cross interaction integrates the two paths. As a challenging validation, we evaluate on epileptic seizure detection across three public datasets (FMCE, HUP, and Helsinki neonatal EEG) under strict subject-disjoint conditions (no leakage). EEG-GraphFrFT consistently outperforms strong baselines (e.g., EEG-Conformer, Mamba) by approximately 2–8 \% in accuracy, while demonstrating robust performance under colored Gaussian noise and channel dropouts, with corresponding improvements in F1 and AUROC. Beyond EEG, the graph fractional operators are task-agnostic and apply broadly to nonstationary graph signals, e.g., traffic sensor networks, climate teleconnections, and multi-asset financial series.

Primary Area: applications to neuroscience & cognitive science

Submission Number: 3686