Parallel Noising in Neural Markov Logic Networks

2026-07-21

AI Summary

Neural Markov Logic Networks (NMLNs) exhibit limited performance when generating large-scale relational graph structures. To address this limitation, this work proposes an enhanced approach that leverages graph neural networks to enrich the expressive power of potential functions and introduces a parallelized noisy training and inference algorithm inspired by parallel tempering MCMC. The proposed method substantially improves the generative capabilities of NMLNs on general graph generation tasks, achieving performance on par with or even surpassing that of state-of-the-art diffusion models. Furthermore, it demonstrates competitive results in small-molecule structure generation compared to specialized sequence-based models, thereby validating its effectiveness and competitiveness in modeling complex relational structures.

Abstract

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.

Problem

• Neural Markov Logic Networks
• generative graph models
• diffusion-based models
• molecular structure generation
• relational structures

Innovation

• Neural Markov Logic Networks
• graph neural networks
• parallel noising
• generative graph models
• parallel-tempering MCMC