Experimental Uncertainty Propagation in Neural Network Extraction in Hadronic Physics

Abstract: Obtaining Compton Form Factors (CFFs) and Transverse Momentum Dependent parton distribution functions (TMDs) from experimental data using neural network-based information extraction requires the precise propagation of experimental errors. Accurate representation of uncertainties and detailed experimental covariance matrices, accounting for both statistical and systematic uncertainties, are essential for high-quality extractions. This paper explores instrumental and analytical contributions to fit and model uncertainties, along with methods for integrating these uncertainties into quantifiable results, ensuring robust extraction of physical observables across local and global datasets. Using pseudodata we demonstrate the critical role of accurate uncertainty propagation in producing meaningful results and advancing our understanding of partonic structure and dynamics inside of hardrons. \keywords{Deep neural networks \and Hadronic Physics \and Transverse momentum dependent parton distributions functions \and Compton form factors \and Uncertainty Analysis