Precise and accurate theoretical predictions are a fundamental ingredient in order to exploit the full potential of the wealth of data from the LHC experiments. In this context, it is particularly important to have a robust determination of the uncertainties on the current determinations of Parton Distribution Functions (PDFs). The NNPDF collaboration has pioneered the usage of Machine Learning (ML) techniques in order to extract PDFs from a finite set of data, a typical example of an inverse problem. In this talk we introduce a framework to analyse the training of Neural Networks, present its application to the PDFs determination, and discuss future research directions.