Learning from Logical Constraints with Lower- and Upper-Bound Arithmetic Circuits

Dierckx, Lucile; Dubray, Alexandre; Nijssen, Siegfried

doi:10.24963/ijcai.2025/558

Learning from Logical Constraints with Lower- and Upper-Bound Arithmetic Circuits

Lucile Dierckx, Alexandre Dubray, Siegfried Nijssen

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Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. Main Track. Pages 5012-5020.

https://doi.org/10.24963/ijcai.2025/558

Keywords

Knowledge Representation and Reasoning: KRR: Learning and reasoning
Uncertainty in AI: UAI: Probabilistic programming
Machine Learning: ML: Neuro-symbolic methods/Abductive Learning
Knowledge Representation and Reasoning: KRR: Knowledge compilation

Abstract

An important class of neuro-symbolic (NeSy) methods relies on knowledge compilation (KC) techniques to transform logical constraints into a differentiable exact arithmetic circuit (AC) that represents all models of a logical formula. However, given the complexity of KC, compiling such exact circuits can be infeasible. Previous works in such cases proposed to compile a circuit for a subset of models. In this work, we will show that gradients calculated on a subset of models can be very far from true gradients. We propose a new framework that calculates gradients based on compiling logical constraints partially in not only a lower-bound circuit but also an upper-bound circuit. We prove that from this pair of ACs, gradients that are within a bounded distance from true gradients can be calculated. Our experiments show that adding the upper-bound AC also helps the learning process in practice, allowing for similar or better generalisation than working solely with fully compiled ACs, even with less than 150 seconds of partial compilation.

Lucile Dierckx, Alexandre Dubray, and Siegfried Nijssen. 2025. Learning from Logical Constraints with Lower- and Upper-Bound Arithmetic Circuits. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25. IJCAI, 5012–5020. https://doi.org/10.24963/ijcai.2025/558

@inproceedings{ijcai2025p558,
  title     = {Learning from Logical Constraints with Lower- and Upper-Bound Arithmetic Circuits},
  author    = {Dierckx, Lucile and Dubray, Alexandre and Nijssen, Siegfried},
  booktitle = {Proceedings of the Thirty-Fourth International Joint Conference on
               Artificial Intelligence, {IJCAI-25}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {James Kwok},
  pages     = {5012--5020},
  year      = {2025},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2025/558},
  url       = {https://doi.org/10.24963/ijcai.2025/558},
}

TY  - CPAPER
TI  - Learning from Logical Constraints with Lower- and Upper-Bound Arithmetic Circuits
AU  - Dierckx, Lucile
AU  - Dubray, Alexandre
AU  - Nijssen, Siegfried
T2  - Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2025
SP  - 5012
EP  - 5020
DO  - 10.24963/ijcai.2025/558
UR  - https://doi.org/10.24963/ijcai.2025/558
ER  -