pTopoFL: Privacy-Preserving Personalised Federated Learning via Persistent Homology

Abstract:

Federated learning (FL) faces two structural tensions: gradient sharing enables datareconstruction 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 PH feature vectors—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, and we establish linear convergence of the Wasserstein-weighted aggregation scheme. Evaluated against FedAvg, FedProx, SCAFFOLD, and pFedMe on a non-IID healthcare scenario (8 hospitals) and a pathological benchmark (10 clients), pTopoFL achieves AUC 0.841 and 0.910 respectively—the highest in both settings—while reducing reconstruction risk 4.5× relative to gradient sharing. Code and data are publicly available at X.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=ibvx4cYhEN&noteId=waNovcxV02

Changes Since Last Submission: This is a revised resubmission of TMLR submission 7784. The following changes have been made: (1) all identifying information has been removed, including author names, affiliations, the GitHub link, the Zenodo DOI, and the acknowledgements section; (2) the duplicate Introduction heading on page 1 has been corrected; (3) Sections 3–6 now each open with a high-level paragraph summarising their content.

Assigned Action Editor: ~Hongchang_Gao1

Submission Number: 8843