PTOPOFL: Privacy-Preserving Personalised Federated Learning via Persistent Homology

TL;DR

PTOPOFL introduces a privacy-preserving federated learning framework that uses persistent homology to replace gradient sharing, enhancing privacy and personalization while maintaining high accuracy in non-IID data scenarios.

Contribution

The paper proposes a novel topology-based descriptor approach for federated learning that reduces information leakage and improves convergence and personalization.

Findings

Achieves higher AUC scores than baseline methods in healthcare and benchmark scenarios.

Reduces data reconstruction risk by a factor of 4.5 compared to gradient sharing.

Proves theoretical bounds on information leakage and convergence.

Abstract

Federated learning (FL) faces two structural tensions: gradient sharing enables data-reconstruction attacks, while non-IID client distributions degrade aggregation quality. We introduce PTOPOFL, a framework that addresses both challenges simultaneously by replacing gradient communication with topological descriptors derived from persistent homology (PH). Clients transmit only 48-dimensional PH feature vectors-compact shape summaries whose many-to-one structure makes inversion provably ill-posed-rather than model gradients. The server performs topology-guided personalised aggregation: clients are clustered by Wasserstein similarity between their PH diagrams, intra-cluster models are topology-weighted,and clusters are blended with a global consensus. We prove an information-contraction theorem showing that PH descriptors leak strictly less mutual information per sample than gradients under strongly convex loss functions, and we establish linear convergence of the Wasserstein-weighted aggregation scheme with an error floor strictly smaller than FedAvg. Evaluated against FedAvg, FedProx, SCAFFOLD, and pFedMe on a non-IID healthcare scenario (8 hospitals, 2 adversarial) and a pathological benchmark (10 clients), PTOPOFL achieves AUC 0.841 and 0.910 respectively-the highest in both settings-while reducing reconstruction risk by a factor of 4.5 relative to gradient sharing. Code is publicly available at https://github.com/MorillaLab/TopoFederatedL and data at https://doi.org/10.5281/zenodo.18827595.