Parton distribution functions

We discuss the determination of the parton substructure of hadrons by casting it as a peculiar form of pattern recognition problem in which the pattern is a probability distribution, and we present the way this problem has been tackled and solved. Specifically, we review the NNPDF approach to PDF determination, which is based on the combination of a Monte Carlo approach with neural networks as basic underlying interpolators. We discuss the current NNPDF methodology, based on genetic minimization, and its validation through closure testing. We then present recent developments in which a hyperoptimized deep-learning framework for PDF determination is being developed, optimized, and tested.