Semantic Objective Functions: A Distribution-Aware Method for Adding Logical Constraints in Deep Learning

Miguel Angel Mendez-Lucero, Enrique Bojorquez Gallardo, Vaishak Belle

2025

Abstract

Issues of safety, explainability, and efficiency are of increasing concern in learning systems deployed with hard and soft constraints. Loss-function based techniques have shown promising results in this area, by embedding logical constraints during neural network training. Through an integration of logic and information geometry, we provide a construction and theoretical framework for these tasks that generalize many approaches. We propose a loss-based method that embeds knowledge—enforces logical constraints—into a machine learning model that outputs probability distributions. This is done by constructing a distribution from the logical formula, and constructing a loss function as a linear combination of the original loss function with the Fisher-Rao distance or Kullback-Leibler divergence to the constraint distribution. This construction is primarily for logical constraints in the form of propositional formulas (Boolean variables), but can be extended to formulas of a first-order language with finite variables over a model with compact domain (categorical and continuous variables), and others statistical models that is to be trained with semantic information. We evaluate our method on a variety of learning tasks, including classification tasks with logic constraints, transferring knowledge from logic formulas, and knowledge distillation.

Paper Citation

in Harvard Style

Mendez-Lucero M., Gallardo E. and Belle V. (2025). Semantic Objective Functions: A Distribution-Aware Method for Adding Logical Constraints in Deep Learning. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART; ISBN 978-989-758-737-5, SciTePress, pages 909-917. DOI: 10.5220/0013229200003890

in Bibtex Style

@conference{icaart25,
author={Miguel Mendez-Lucero and Enrique Gallardo and Vaishak Belle},
title={Semantic Objective Functions: A Distribution-Aware Method for Adding Logical Constraints in Deep Learning},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART},
year={2025},
pages={909-917},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013229200003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART
TI - Semantic Objective Functions: A Distribution-Aware Method for Adding Logical Constraints in Deep Learning
SN - 978-989-758-737-5
AU - Mendez-Lucero M.
AU - Gallardo E.
AU - Belle V.
PY - 2025
SP - 909
EP - 917
DO - 10.5220/0013229200003890
PB - SciTePress