GraphFSA: A Finite State Automaton Framework for Algorithmic Learning on Graphs

TL;DR

GraphFSA introduces a novel framework that learns finite state automata on graph nodes, enabling better representation and generalization of complex graph algorithms, demonstrated through cellular automata and synthetic problem evaluations.

Contribution

The paper presents GraphFSA, a new framework for learning finite state automata on graphs, addressing limitations of existing architectures in representing discrete state transitions.

Findings

GraphFSA effectively learns automata for cellular automata problems.

The framework demonstrates strong generalization and extrapolation abilities.

It provides an alternative approach for representing complex graph algorithms.

Abstract

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.