Warm Starting State-Space Models with Automata Learning
arXiv:2603.05694v1 Announce Type: new 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 initial
arXiv:2603.05694v1 Announce Type: new 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.
Executive Summary
This article explores the connection between automata learning and state-space models (SSMs). By establishing a formal correspondence between Moore machines and SSMs, the authors demonstrate that SSMs can preserve the symbolic structure and input-output behavior of automata. However, the results show that SSMs require more data than symbolic methods to learn automata, suggesting that symbolic structure provides a strong inductive bias. The authors propose a hybrid approach that combines the strengths of both methods to learn complex systems efficiently. The results demonstrate faster and better convergence compared to randomly initialized models. This work has significant implications for the application of automata learning in continuous domains.
Key Points
- ▸ Moore machines can be exactly realized as state-space models (SSMs)
- ▸ SSMs preserve the symbolic structure and input-output behavior of automata
- ▸ SSMs require more data than symbolic methods to learn automata
- ▸ A hybrid approach combining automata learning and SSMs is proposed for efficient learning
- ▸ Faster and better convergence is achieved with the hybrid approach compared to randomly initialized models
Merits
Establishing a formal correspondence between Moore machines and SSMs
This connection enables the application of automata learning in continuous domains, which is a significant contribution to the field.
Demonstrating the effectiveness of a hybrid approach
The results show that combining automata learning and SSMs can lead to faster and better convergence, making it a promising method for learning complex systems.
Demerits
Limited generalizability to other types of automata
The results are specifically focused on Moore machines, and it is unclear whether the findings can be extended to other types of automata.
Potential over-reliance on symbolic structure
The article suggests that symbolic structure provides a strong inductive bias, but it is unclear whether this approach may become overly restrictive in certain situations.
Expert Commentary
The article presents a novel connection between automata learning and state-space models, which has significant implications for the application of automata learning in continuous domains. The proposed hybrid approach is a promising method for learning complex systems efficiently, and the results demonstrate its effectiveness. However, further research is needed to fully understand the limitations and potential applications of this approach. The article also raises important questions about the role of symbolic structure in machine learning algorithms, which will be crucial for policymakers and researchers in the field.
Recommendations
- ✓ Future research should focus on extending the findings to other types of automata and exploring the potential applications of the hybrid approach in various fields.
- ✓ The development of more efficient and effective machine learning algorithms for complex systems should be a priority, and the proposed hybrid approach is a promising direction to pursue.