Learning Graph Weighted Models on Pictures

TL;DR

This paper explores learning Graph Weighted Models (GWMs) over picture graphs, demonstrating that gradient-based methods can effectively learn these models for simple image languages like Bars & Stripes.

Contribution

It introduces the problem of learning GWMs on 2D picture graphs and provides experimental evidence that gradient-based learning is feasible for simple image languages.

Findings

Gradient-based methods can learn GWMs for picture languages.

GWMs can model simple 2D image languages like Bars & Stripes.

Potential for extending learning to more complex graph families.

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.