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.

翻译：本文提出逻辑张量网络增强的生成对抗网络（LTN-GAN），该创新框架通过引入逻辑张量网络（LTNs）在样本生成过程中强制执行领域特定的逻辑约束，从而增强生成对抗网络（GANs）的性能。尽管GANs在生成逼真数据方面已取得显著成功，但其通常缺乏融入先验知识或保障逻辑一致性的机制，这限制了其在需要遵循规则领域中的应用。LTNs为将一阶逻辑与神经网络相结合提供了原则性方法，使模型能够对逻辑约束进行推理并满足其要求。通过融合GANs在逼真数据合成方面的优势与LTNs在逻辑推理方面的能力，我们深入理解了逻辑约束如何影响生成过程，同时提升了生成样本的多样性与逻辑一致性。我们在多个数据集上评估LTN-GAN，包括合成数据集（高斯分布、网格结构、环形结构）和MNIST数据集，实验表明我们的模型在遵循预定义逻辑约束方面显著优于传统GANs，同时保持了生成样本的质量与多样性。本工作凸显了神经符号方法在知识密集型领域增强生成建模的潜力。