用自动机学习结果初始化状态空间模型，显著提升训练速度与精度。
Warm Starting State-Space Models with Automata Learning
- 将符号自动机转化为连续空间的状态空间模型，建立形式化对应关系。
- 符号结构能大幅降低数据需求，传统SSM需海量数据仍难学出状态结构。
- 基于符号学习的初始化使模型收敛快2-5倍，适合复杂系统高效建模。
我们证明了摩尔机可被精确实现为状态空间模型（SSMs），建立了符号自动机与连续机器学习架构之间的形式对应关系。这些摩尔-SSMs保持原摩尔机的完整符号结构和输入输出行为，但在欧氏空间中运行。基于该对应关系，我们对比了SSM在被动与主动自动机学习下的训练表现。在从SYNTCOMP基准恢复自动机时，发现SSM所需数据量比符号方法多出数个数量级，且无法学习出状态结构。这表明符号结构提供了强大的归纳偏置。我们据此结合自动机学习与SSM的优势，高效学习复杂系统：从SYNTCOMP中学习一组仲裁器的自适应仲裁策略，并以符号学习得到的近似解初始化SSM，相比随机初始化模型，收敛速度提升2-5倍，测试精度更高。本工作将自动机学习拓展至连续空间，为复杂场景下高效学习提供了可解释、可引导的范式。
原文摘要 · Abstract (English)
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.
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