Learning Graph Weighted Models on Pictures
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Proceedings of The 14th International Conference on Grammatical Inference 2018, PMLR 93:104117, 2019.
Abstract
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 2dimensional 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 gradientbased methods. Our results suggest that this is indeed possible and that investigating the use of gradientbased methods to learn picture series and functions computed by GWMs over other families of graphs could be a fruitful direction.
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