Learning Graph Weighted Models on Pictures

Philip Amortila, Guillaume Rabusseau
Proceedings of The 14th International Conference on Grammatical Inference 2018, PMLR 93:104-117, 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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v93-amortila19a, title = {Learning Graph Weighted Models on Pictures}, author = {Amortila, Philip and Rabusseau, Guillaume}, booktitle = {Proceedings of The 14th International Conference on Grammatical Inference 2018}, pages = {104--117}, year = {2019}, editor = {Unold, Olgierd and Dyrka, Witold and Wieczorek, Wojciech}, volume = {93}, series = {Proceedings of Machine Learning Research}, month = {feb}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v93/amortila19a/amortila19a.pdf}, url = {https://proceedings.mlr.press/v93/amortila19a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Learning Graph Weighted Models on Pictures %A Philip Amortila %A Guillaume Rabusseau %B Proceedings of The 14th International Conference on Grammatical Inference 2018 %C Proceedings of Machine Learning Research %D 2019 %E Olgierd Unold %E Witold Dyrka %E Wojciech Wieczorek %F pmlr-v93-amortila19a %I PMLR %P 104--117 %U https://proceedings.mlr.press/v93/amortila19a.html %V 93 %X 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.
APA
Amortila, P. & Rabusseau, G.. (2019). Learning Graph Weighted Models on Pictures. Proceedings of The 14th International Conference on Grammatical Inference 2018, in Proceedings of Machine Learning Research 93:104-117 Available from https://proceedings.mlr.press/v93/amortila19a.html.

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