Relational Neurosymbolic Markov Models

TL;DR

This paper introduces relational neurosymbolic Markov models (NeSy-MMs), which integrate logical constraints into sequential models, enabling scalable, interpretable, and trustworthy AI solutions that outperform current neurosymbolic methods.

Contribution

The paper presents a novel class of end-to-end differentiable sequential models that incorporate relational logical constraints with scalable inference and learning strategies.

Findings

NeSy-MMs outperform state-of-the-art neurosymbolic AI in sequential tasks.

Models provide strong guarantees for desired properties.

Constraints can be adapted at test time for out-of-distribution scenarios.

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.