In this contribution we present a status report on the recent progress towards an analysis of nuclear parton distribution functions (nPDFs) using the NNPDF methodology. We discuss how the NNPDF fitting approach can be extended to account for the dependence on the atomic mass number $A$, and introduce novel algorithms to improve the training of the neural network parameters within the NNPDF framework. Finally, we present preliminary results of a nPDF fit to neutral current deep-inelastic lepton-nucleus scattering data, and demonstrate how one can validate the new fitting methodology by means of closure tests.
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