Parton distribution from NTK analysis - Amedeo CHIEFA

The talk by Amedeo Chieffa presents a novel application of Neural Tangent Kernel (NTK) analysis to the determination of parton distribution functions (PDFs) from experimental data. PDFs are essential for predicting proton collisions but cannot be computed perturbatively; they must be extracted via inverse problems. The speaker introduces the factorization formula and explains that PDF extraction is an ill-defined inverse problem due to limited data and a continuous unknown function. The standard approaches include Bayesian methods and parametric regression, with NNPDF using neural networks. The talk focuses on understanding the learning process of the neural network during training, using the gradient flow and the NTK. The NTK is a matrix that encodes the dependence on the network parameters, and its spectrum shows a hierarchy with few dominant directions. The speaker shows that during training, the NTK evolves, but eventually becomes constant (lazy regime). They derive an analytic solution for the network output in the lazy regime, which factorizes contributions from the initial function and the data. They validate this with closure tests and show that the NTK aligns with the physics encoded in the data. The analytic solution can be used to monitor training and to separate parameterization bias from data-driven information. The speaker concludes that while the NTK cannot be directly used for real PDF extraction due to the non-constant NTK, it serves as a diagnostic tool. Future work includes generalizing to nonlinear predictions and other parameterizations.