# Constraint-Based Visual Generation

arXiv: https://arxiv.org/abs/1807.09202 · HTML: https://mlsanity.com/paper/1807.09202/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression](https://mlsanity.com/paper/2312.14237/) (2023)
- [AI Descartes: Combining Data and Theory for Derivable Scientific Discovery](https://mlsanity.com/paper/2109.01634/) (2021)
- [The Need for Verification in AI-Driven Scientific Discovery](https://mlsanity.com/paper/2509.01398/) (2025)
- [Out of Distribution Reasoning by Weakly-Supervised Disentangled Logic Variational Autoencoder](https://mlsanity.com/paper/2210.09959/) (2022)

## Abstract (arXiv)

In the last few years the systematic adoption of deep learning to visual generation has produced impressive results that, amongst others, definitely benefit from the massive exploration of convolutional architectures. In this paper, we propose a general approach to visual generation that combines learning capabilities with logic descriptions of the target to be generated. The process of generation is regarded as a constrained satisfaction problem, where the constraints describe a set of properties that characterize the target. Interestingly, the constraints can also involve logic variables, while all of them are converted into real-valued functions by means of the t-norm theory. We use deep architectures to model the involved variables, and propose a computational scheme where the learning process carries out a satisfaction of the constraints. We propose some examples in which the theory can naturally be used, including the modeling of GAN and auto-encoders, and report promising results in problems with the generation of handwritten characters and face transformations.