Relational Neurosymbolic Markov Models
Lennert De Smet, Gabriele Venturato, Luc De Raedt, Giuseppe Marra
Abstract
Sequential problems are ubiquitous in AI, such as in reinforcement learning or natural language processing. State-of-the-art deep sequential models, like transformers, excel in these settings but fail to guarantee the satisfaction of constraints necessary for trustworthy deployment. In contrast, neurosymbolic AI (NeSy) provides a sound formalism to enforce constraints in deep probabilistic models but scales exponentially on sequential problems. To overcome these limitations, we introduce relational neurosymbolic Markov models (NeSy-MMs), a new class of end-to-end differentiable sequential models that integrate and provably satisfy relational logical constraints. We propose a strategy for inference and learning that scales on sequential settings, and that combines approximate Bayesian inference, automated reasoning, and gradient estimation. Our experiments show that NeSy-MMs can solve problems beyond the current state-of-the-art in neurosymbolic AI and still provide strong guarantees with respect to desired properties. Moreover, we show that our models are more interpretable and that constraints can be adapted at test time to out-of-distribution scenarios.
BibTeX
@article{De Smet_Venturato_De Raedt_Marra_2025, title={Relational Neurosymbolic Markov Models}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/33777}, DOI={10.1609/aaai.v39i15.33777}, abstractNote={Sequential problems are ubiquitous in AI, such as in reinforcement learning or natural language processing. State-of-the-art deep sequential models, like transformers, excel in these settings but fail to guarantee the satisfaction of constraints necessary for trustworthy deployment. In contrast, neurosymbolic AI (NeSy) provides a sound formalism to enforce constraints in deep probabilistic models but scales exponentially on sequential problems. To overcome these limitations, we introduce relational neurosymbolic Markov models (NeSy-MMs), a new class of end-to-end differentiable sequential models that integrate and provably satisfy relational logical constraints. We propose a strategy for inference and learning that scales on sequential settings, and that combines approximate Bayesian inference, automated reasoning, and gradient estimation. Our experiments show that NeSy-MMs can solve problems beyond the current state-of-the-art in neurosymbolic AI and still provide strong guarantees with respect to desired properties. Moreover, we show that our models are more interpretable and that constraints can be adapted at test time to out-of-distribution scenarios.}, number={15}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={De Smet, Lennert and Venturato, Gabriele and De Raedt, Luc and Marra, Giuseppe}, year={2025}, month={Apr.}, pages={16181-16189} }