A Nivat Theorem for Weighted Picture Automata and Weighted MSO Logic

Babari, Parvaneh; Droste, Manfred

doi:10.1007/978-3-319-15579-1_55

Cited by 3 publications

(1 citation statement)

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“…Regular picture languages can equivalently be described in terms of automata, sets of tiles, rational operations, or monadic second order logic Inoue and Nakamura, 1977;Latteux and Simplot, 1997). The extension of regular picture languages to the quantitative setting led to the definition of recognizable picture series whose theoretical study has been of recent interest (Bozapalidis and Grammatikopoulou, 2005;Mäurer, 2005;Fichtner, 2011;Babari and Droste, 2015). Recognizable picture series were first introduced in (Bozapalidis and Grammatikopoulou, 2005) by means of Weighted Picture Automata.…”

Section: Weighted Picture Automatonmentioning

confidence: 99%

Learning Graph Weighted Models on Pictures

Amortila,

Rabusseau

2018

Preprint

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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 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.

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Section: Weighted Picture Automatonmentioning

confidence: 99%