Warm Starting State-Space Models with Automata Learning

TL;DR

This paper establishes a formal link between automata and state-space models, showing how symbolic automata can inform continuous models for more efficient learning of complex systems.

Contribution

It proves Moore machines can be exactly realized as state-space models, enabling hybrid approaches that leverage symbolic structure for improved learning efficiency.

Findings

SSMs require more data than symbolic methods for automata recovery

Initializing SSMs with automata approximations improves learning speed and accuracy

Hybrid automata-SSM methods outperform random initialization in complex system learning

Abstract

We prove that Moore machines can be exactly realized as state-space models (SSMs), establishing a formal correspondence between symbolic automata and these continuous machine learning architectures. These Moore-SSMs preserve both the complete symbolic structure and input-output behavior of the original Moore machine, but operate in Euclidean space. With this correspondence, we compare the training of SSMs with both passive and active automata learning. In recovering automata from the SYNTCOMP benchmark, we show that SSMs require orders of magnitude more data than symbolic methods and fail to learn state structure. This suggests that symbolic structure provides a strong inductive bias for learning these systems. We leverage this insight to combine the strengths of both automata learning and SSMs in order to learn complex systems efficiently. We learn an adaptive arbitration policy on a suite of arbiters from SYNTCOMP and show that initializing SSMs with symbolically-learned approximations learn both faster and better. We see 2-5 times faster convergence compared to randomly initialized models and better overall model accuracies on test data. Our work lifts automata learning out of purely discrete spaces, enabling principled exploitation of symbolic structure in continuous domains for efficiently learning in complex settings.