# NeSyA: Neurosymbolic Automata

arXiv: https://arxiv.org/abs/2412.07331 · HTML: https://mlsanity.com/paper/2412.07331/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Tractable Control for Autoregressive Language Generation](https://mlsanity.com/paper/2304.07438/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints](https://mlsanity.com/paper/2312.03905/) (2023)
- [DeepDFA: Automata Learning through Neural Probabilistic Relaxations](https://mlsanity.com/paper/2408.08622/) (2024)

## Built on by (most cited first, 10 of 10)

- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [NeuS-QA: Grounding Long-Form Video Understanding in Temporal Logic and Neuro-Symbolic Reasoning](https://mlsanity.com/paper/2509.18041/) (2025)
- [Neuro-Symbolic Predictive Process Monitoring](https://mlsanity.com/paper/2509.00834/) (2025)
- [A Neuro-Symbolic Framework for Sequence Classification with Relational and Temporal Knowledge](https://mlsanity.com/paper/2505.05106/) (2025)
- [RT-NeuS: Towards Real-Time Neuro-Symbolic Video Understanding via Adaptive Temporal Verification](https://mlsanity.com/paper/2602.23553/) (2026)
- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)
- [LTLZinc: a Benchmarking Framework for Continual Learning and Neuro-Symbolic Temporal Reasoning](https://mlsanity.com/paper/2507.17482/) (2025)
- [DeepDFA: Injecting Temporal Logic in Deep Learning for Sequential Subsymbolic Applications](https://mlsanity.com/paper/2602.03486/) (2026)
- [Neuro-Symbolic Injection of LTLf Constraints in Autoregressive Reinforcement Learning Policies](https://mlsanity.com/paper/2606.08312/) (2026)
- [Neurosymbolic Learning of Interpretable World Models](https://mlsanity.com/paper/2610.19955/) (2026)

## Abstract (arXiv)

Neurosymbolic (NeSy) AI has emerged as a promising direction to integrate neural and symbolic reasoning. Unfortunately, little effort has been given to developing NeSy systems tailored to sequential/temporal problems. We identify symbolic automata (which combine the power of automata for temporal reasoning with that of propositional logic for static reasoning) as a suitable formalism for expressing knowledge in temporal domains. Focusing on the task of sequence classification and tagging we show that symbolic automata can be integrated with neural-based perception, under probabilistic semantics towards an end-to-end differentiable model. Our proposed hybrid model, termed NeSyA (Neuro Symbolic Automata) is shown to either scale or perform more accurately than previous NeSy systems in a synthetic benchmark and to provide benefits in terms of generalization compared to purely neural systems in a real-world event recognition task.