# Learning Logistic Circuits

arXiv: https://arxiv.org/abs/1902.10798 · HTML: https://mlsanity.com/paper/1902.10798/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 12 of 12)

- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Probabilistic Sufficient Explanations](https://mlsanity.com/paper/2105.10118/) (2021)
- [Coalesced Multi-Output Tsetlin Machines with Clause Sharing](https://mlsanity.com/paper/2108.07594/) (2021)
- [Looped ReLU MLPs May Be All You Need as Practical Programmable Computers](https://mlsanity.com/paper/2410.09375/) (2024)
- [HyperSPNs: Compact and Expressive Probabilistic Circuits](https://mlsanity.com/paper/2112.00914/) (2021)
- [Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Size](https://mlsanity.com/paper/2301.08190/) (2023)
- [Probabilistic Circuits That Know What They Don't Know](https://mlsanity.com/paper/2302.06544/) (2023)
- [Probabilistic Neural Circuits](https://mlsanity.com/paper/2403.06235/) (2024)
- [ProbLP: A framework for low-precision probabilistic inference](https://mlsanity.com/paper/2103.00216/) (2021)
- [Neural Logic Networks for Interpretable Classification](https://mlsanity.com/paper/2508.08172/) (2025)
- [KnowSafe: Combined Knowledge and Data Driven Hazard Mitigation in Artificial Pancreas Systems](https://mlsanity.com/paper/2311.07460/) (2023)
- [REASON: Accelerating Probabilistic Logical Reasoning for Scalable Neuro-Symbolic Intelligence](https://mlsanity.com/paper/2601.20784/) (2026)

## Abstract (arXiv)

This paper proposes a new classification model called logistic circuits. On MNIST and Fashion datasets, our learning algorithm outperforms neural networks that have an order of magnitude more parameters. Yet, logistic circuits have a distinct origin in symbolic AI, forming a discriminative counterpart to probabilistic-logical circuits such as ACs, SPNs, and PSDDs. We show that parameter learning for logistic circuits is convex optimization, and that a simple local search algorithm can induce strong model structures from data.