# Federated Learning with Energy-Based Structured Probabilistic Inference

arXiv: https://arxiv.org/abs/2606.30161 · HTML: https://mlsanity.com/paper/2606.30161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [FLUX: Efficient Descriptor-Driven Clustered Federated Learning under Arbitrary Distribution Shifts](https://mlsanity.com/paper/2511.22305/) (2025)
- [Federated Behavioural Planes: Explaining the Evolution of Client Behaviour in Federated Learning](https://mlsanity.com/paper/2405.15632/) (2024)
- [Federated Learning with Profile Mapping under Distribution Shifts and Drifts](https://mlsanity.com/paper/2602.07671/) (2026)

## Abstract (arXiv)

Federated Learning (FL) enables multiple clients to collaboratively train machine learning models without sharing their local data. However, heterogeneity in client data and the presence of unreliable or adversarial updates make effective server aggregation challenging, motivating methods that adapt client contributions according to their reliability and relationships. In this work, we formulate server aggregation in FL as structured probabilistic inference using conditional random fields. We represent clients as nodes in a graph and define unary and pairwise energy potentials. Unary potentials capture individual client properties, while pairwise potentials encode similarities between clients. This formulation treats individual client evidence and pairwise relationships as coupled evidence in a joint inference problem, allowing client reliabilities to be inferred collectively and the resulting estimates to guide aggregation. Where most FL methods target a single challenge, FedCRF's inferred reliabilities and affinities provide one common representation for global aggregation, Byzantine robustness, clustered FL, and personalized FL. With a single set of hyperparameters, it is competitive with or outperforms specialized methods on CIFAR-10, FEMNIST, and Fed-ISIC2019 across diverse forms of client heterogeneity and unreliability.