# Federated Neuro-Symbolic Learning

arXiv: https://arxiv.org/abs/2308.15324 · HTML: https://mlsanity.com/paper/2308.15324/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [FedMD: Heterogenous Federated Learning via Model Distillation](https://mlsanity.com/paper/1910.03581/) (2019)
- [Personalized Cross-Silo Federated Learning on Non-IID Data](https://mlsanity.com/paper/2007.03797/) (2020)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [Personalized Federated Learning via Variational Bayesian Inference](https://mlsanity.com/paper/2206.07977/) (2022)
- [Learning Reasoning Strategies in End-to-End Differentiable Proving](https://mlsanity.com/paper/2007.06477/) (2020)
- [Personalized Federated Learning for Intelligent IoT Applications: A Cloud-Edge based Framework](https://mlsanity.com/paper/2002.10671/) (2020)
- [Federated Graph Neural Networks: Overview, Techniques and Challenges](https://mlsanity.com/paper/2202.07256/) (2022)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [A Bayesian Federated Learning Framework with Online Laplace Approximation](https://mlsanity.com/paper/2102.01936/) (2021)
- [DWIE: an entity-centric dataset for multi-task document-level information extraction](https://mlsanity.com/paper/2009.12626/) (2020)
- [Connecting Language and Knowledge Bases with Embedding Models for Relation Extraction](https://mlsanity.com/paper/1307.7973/) (2013)
- [Learning Logic Rules for Document-level Relation Extraction](https://mlsanity.com/paper/2111.05407/) (2021)
- [An Expectation-Maximization Perspective on Federated Learning](https://mlsanity.com/paper/2111.10192/) (2021)
- [Ruleformer: Context-aware Differentiable Rule Mining over Knowledge Graph](https://mlsanity.com/paper/2209.05815/) (2022)
- [Differentiable Learning of Logical Rules for Knowledge Base Reasoning](https://mlsanity.com/paper/1702.08367/) (2017)
- [Teaching Probabilistic Logical Reasoning to Transformers](https://mlsanity.com/paper/2305.13179/) (2023)
- [LR-XFL: Logical Reasoning-based Explainable Federated Learning](https://mlsanity.com/paper/2308.12681/) (2023)

## Built on by (most cited first, 2 of 2)

- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era](https://mlsanity.com/paper/2603.03177/) (2026)

## Abstract (arXiv)

Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL learning involves directly acquiring data from downstream tasks, which is not feasible for federated learning (FL). To address this limitation, we shift the focus from such a one-to-one interactive neuro-symbolic paradigm to one-to-many Federated Neuro-Symbolic Learning framework (FedNSL) with latent variables as the FL communication medium. Built on the basis of our novel reformulation of the NSL theory, FedNSL is capable of identifying and addressing rule distribution heterogeneity through a simple and effective Kullback-Leibler (KL) divergence constraint on rule distribution applicable under the FL setting. It further theoretically adjusts variational expectation maximization (V-EM) to reduce the rule search space across domains. This is the first incorporation of distribution-coupled bilevel optimization into FL. Extensive experiments based on both synthetic and real-world data demonstrate significant advantages of FedNSL compared to five state-of-the-art methods. It outperforms the best baseline by 17% and 29% in terms of unbalanced average training accuracy and unseen average testing accuracy, respectively.