Graph Neural Networks Trained on Null Signal for Angle Reconstruction in X-ray Polarimetry
Scientific real detectors often produce sparse, irregular data defined on non-Euclidean domains, where conventional convolutional neural networks (CNNs) impose geometric biases that distort physical observables. In X-ray polarimetry, such distortions can mimic polarization signals at the percent level, critically limiting measurement fidelity. We consider a framework based on Graph Neural Networks (GNNs) for reconstructing photoelectron emission angles from Gas Pixel Detectors, operating directly on their native sparse hexagonal topology. The network is trained solely on unpolarized simulated data and integrates rotational data augmentation, ensemble averaging, and modulation-aware model selection to reduce spurious angular modulation. Despite never encountering polarized examples, the model is able to recover the overall structure of polarized signals. Compared with the classical Method of Moments (MoM), an analytical approach to track angle reconstruction, the proposed GNN achieves lower per-track error but yields worse performance for polarimetry, revealing a mismatch between local reconstruction accuracy and global polarimetric performance. Compared to CNN-based approaches, the framework shows competitive performance on both unpolarized and polarized reconstructions, despite being trained in a more challenging power-law energy distribution. These results position the method as a diagnostic tool to highlight the limitations and trade-offs of learning-based approaches for X-ray-polarimetry signal reconstruction.