Sheaf HyperNetworks for Personalized Federated Learning

TL;DR

This paper introduces Sheaf HyperNetworks, a novel approach combining sheaf theory with hypernetworks to enhance personalized federated learning, especially when client relation graphs are unavailable, leading to improved performance in diverse tasks.

Contribution

The paper proposes Sheaf HyperNetworks, a new class of hypernetworks integrating sheaf theory to address limitations of existing GHNs in PFL scenarios without client relation graphs.

Findings

SHNs outperform existing PFL methods in non-IID tasks.

SHNs achieve up to 2.7% accuracy improvement.

SHNs reduce mean squared error by up to 5.3%.

Abstract

Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated learning. Despite GNNs and HNs being individually successful, we show that GHNs present problems compromising their performance, such as over-smoothing and heterophily. Moreover, we cannot apply GHNs directly to personalized federated learning (PFL) scenarios, where a priori client relation graph may be absent, private, or inaccessible. To mitigate these limitations in the context of PFL, we propose a novel class of HNs, sheaf hypernetworks (SHNs), which combine cellular sheaf theory with HNs to improve parameter sharing for PFL. We thoroughly evaluate SHNs across diverse PFL tasks, including multi-class classification, traffic and weather forecasting. Additionally, we provide a methodology for constructing client relation graphs in scenarios where such graphs are unavailable. We show that SHNs consistently outperform existing PFL solutions in complex non-IID scenarios. While the baselines' performance fluctuates depending on the task, SHNs show improvements of up to 2.7% in accuracy and 5.3% in lower mean squared error over the best-performing baseline.