  Graph Weighted Models (GWMs) have recently been proposed as a natural
generalization of weighted automata over strings and trees to arbitrary
families of labeled graphs (and hypergraphs). A GWM generically associates a
labeled graph with a tensor network and computes a value by successive
contractions directed by its edges. In this paper, we consider the problem of
learning GWMs defined over the graph family of pictures (or 2-dimensional
words). As a proof of concept, we consider regression and classification tasks
over the simple Bars & Stripes and Shifting Bits picture languages and provide
an experimental study investigating whether these languages can be learned in
the form of a GWM from positive and negative examples using gradient-based
methods. Our results suggest that this is indeed possible and that
investigating the use of gradient-based methods to learn picture series and
functions computed by GWMs over other families of graphs could be a fruitful
direction.
