# Warm Starting State-Space Models with Automata Learning

arXiv: https://arxiv.org/abs/2603.05694 · HTML: https://mlsanity.com/paper/2603.05694/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Formal Scenario-Based Testing of Autonomous Vehicles: From Simulation to the Real World](https://mlsanity.com/paper/2003.07739/) (2020)
- [From Spot 2.0 to Spot 2.10: What's New?](https://mlsanity.com/paper/2206.11366/) (2022)
- [Weighted Automata Extraction from Recurrent Neural Networks via Regression on State Spaces](https://mlsanity.com/paper/1904.02931/) (2019)
- [DL2: A Deep Learning-driven Scheduler for Deep Learning Clusters](https://mlsanity.com/paper/1909.06040/) (2019)
- [Extracting Weighted Finite Automata from Recurrent Neural Networks for Natural Languages](https://mlsanity.com/paper/2206.14621/) (2022)
- [Connecting Weighted Automata, Tensor Networks and Recurrent Neural Networks through Spectral Learning](https://mlsanity.com/paper/2010.10029/) (2020)
- [Bisimulation Learning](https://mlsanity.com/paper/2405.15723/) (2024)
- [Execution and monitoring of HOA automata with HOAX](https://mlsanity.com/paper/2507.11126/) (2025)

## Built on by (most cited first, 1 of 1)

- [Logic-Gated Time-Shared Feedforward Networks for Alternating Finite Automata: Exact Simulation and Learnability](https://mlsanity.com/paper/2604.01228/) (2026)

## Abstract (arXiv)

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.