Logic Tensor Network-Enhanced Generative Adversarial Network

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the challenge of integrating domain-specific logical rules into generative adversarial networks (GANs), which often produce logically inconsistent samples in knowledge-intensive scenarios. To bridge this gap, the authors propose embedding Logic Tensor Networks (LTNs) into the GAN framework, enabling the explicit incorporation of differentiable first-order logic constraints during generation. This integration facilitates joint optimization of logical consistency and data fidelity through end-to-end training. As the first approach to combine LTNs—a neuro-symbolic method—with GANs, the proposed model demonstrates superior adherence to prescribed logical rules while preserving sample diversity and visual quality. Empirical validation on synthetic datasets (Gaussian, Grid, Rings) and MNIST confirms that the generated samples significantly outperform those of conventional GANs in satisfying logical constraints, thereby expanding the applicability of generative models to knowledge-driven tasks.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Generation
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

In this paper, we introduce Logic Tensor Network-Enhanced Generative Adversarial Network (LTN-GAN), a novel framework that enhances Generative Adversarial Networks (GANs) by incorporating Logic Tensor Networks (LTNs) to enforce domain-specific logical constraints during the sample generation process. Although GANs have shown remarkable success in generating realistic data, they often lack mechanisms to incorporate prior knowledge or enforce logical consistency, limiting their applicability in domains requiring rule adherence. LTNs provide a principled way to integrate first-order logic with neural networks, enabling models to reason over and satisfy logical constraints. By combining the strengths of GANs for realistic data synthesis with LTNs for logical reasoning, we gain valuable insights into how logical constraints influence the generative process while improving both the diversity and logical consistency of the generated samples. We evaluate LTN-GAN across multiple datasets, including synthetic datasets (gaussian, grid, rings) and the MNIST dataset, demonstrating that our model significantly outperforms traditional GANs in terms of adherence to predefined logical constraints while maintaining the quality and diversity of generated samples. This work highlights the potential of neuro-symbolic approaches to enhance generative modeling in knowledge-intensive domains.

Problem

• Generative Adversarial Networks
• logical constraints
• prior knowledge
• rule adherence
• generative modeling

Innovation

• Logic Tensor Networks
• Generative Adversarial Networks
• Neuro-symbolic AI
• Logical Constraints
• First-order Logic