# Logic Tensor Network-Enhanced Generative Adversarial Network

arXiv: https://arxiv.org/abs/2601.03839 · HTML: https://mlsanity.com/paper/2601.03839/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 24 of 24)

- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [Vitruvion: A Generative Model of Parametric CAD Sketches](https://mlsanity.com/paper/2109.14124/) (2021)
- [Gradient-Based Constrained Sampling from Language Models](https://mlsanity.com/paper/2205.12558/) (2022)
- [Generative Neurosymbolic Machines](https://mlsanity.com/paper/2010.12152/) (2020)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models](https://mlsanity.com/paper/2209.07568/) (2022)
- [How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data](https://mlsanity.com/paper/2402.04823/) (2024)
- [Efficient Generation of Structured Objects with Constrained Adversarial Networks](https://mlsanity.com/paper/2007.13197/) (2020)
- [Deep Generative Models with Learnable Knowledge Constraints](https://mlsanity.com/paper/1806.09764/) (2018)
- [A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints](https://mlsanity.com/paper/2312.03905/) (2023)
- [Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints](https://mlsanity.com/paper/2502.18237/) (2025)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)
- [Neuro-symbolic Learning Yielding Logical Constraints](https://mlsanity.com/paper/2410.20957/) (2024)
- [Constrained Generative Adversarial Networks for Interactive Image Generation](https://mlsanity.com/paper/1904.02526/) (2019)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [BFGAN: Backward and Forward Generative Adversarial Networks for Lexically Constrained Sentence Generation](https://mlsanity.com/paper/1806.08097/) (2018)
- [Goal-directed Generation of Discrete Structures with Conditional Generative Models](https://mlsanity.com/paper/2010.02311/) (2020)
- [Enforcing Deterministic Constraints on Generative Adversarial Networks for Emulating Physical Systems](https://mlsanity.com/paper/1911.06671/) (2019)
- [Semantic Objective Functions: A distribution-aware method for adding logical constraints in deep learning](https://mlsanity.com/paper/2405.15789/) (2024)
- [GenCO: Generating Diverse Designs with Combinatorial Constraints](https://mlsanity.com/paper/2310.02442/) (2023)
- [Generating by Understanding: Neural Visual Generation with Logical Symbol Groundings](https://mlsanity.com/paper/2310.17451/) (2023)

## Built on by (most cited first, 3 of 3)

- [sLTN: Structural Logic Tensor Networks](https://mlsanity.com/paper/2608.11136/) (2026)
- [Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs](https://mlsanity.com/paper/2608.21605/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

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.