# A Hybrid Framework for Healing Semigroups with Machine Learning

arXiv: https://arxiv.org/abs/2509.01763 · HTML: https://mlsanity.com/paper/2509.01763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)
- [Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theory](https://mlsanity.com/paper/2402.15326/) (2024)
- [DUE: A Deep Learning Framework and Library for Modeling Unknown Equations](https://mlsanity.com/paper/2504.10373/) (2025)
- [Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroups](https://mlsanity.com/paper/2410.14477/) (2024)
- [Efficiently learning and sampling multimodal distributions with data-based initialization](https://mlsanity.com/paper/2411.09117/) (2024)
- [Prediction error certification for PINNs: Theory, computation, and application to Stokes flow](https://mlsanity.com/paper/2508.07994/) (2025)
- [A Neural Network for Semigroups](https://mlsanity.com/paper/2103.07388/) (2021)
- [On the contraction properties of Sinkhorn semigroups](https://mlsanity.com/paper/2503.09887/) (2025)

## Abstract (arXiv)

In this paper, we propose a hybrid framework that heals corrupted finite semigroups, combining deterministic repair strategies with Machine Learning using a Random Forest Classifier. Corruption in these tables breaks associativity and invalidates the algebraic structure. Deterministic methods work for small cardinality n and low corruption but degrade rapidly. Our experiments, carried out on Mace4-generated data sets, demonstrate that our hybrid framework achieves higher healing rates than deterministic-only and ML-only baselines. At a corruption percentage of p=15%, our framework healed 95% of semigroups up to cardinality n=6 and 60% at n=10.