PTOPOFL: Privacy-Preserving Personalised Federated Learning via Persistent Homology
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arXiv
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| Format: | Preprint |
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2026
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| author | Vomo-Donfack, Kelly L Hoszu, Adryel Ginot, Grégory Morilla, Ian |
| author_facet | Vomo-Donfack, Kelly L Hoszu, Adryel Ginot, Grégory Morilla, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04323 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PTOPOFL: Privacy-Preserving Personalised Federated Learning via Persistent Homology Vomo-Donfack, Kelly L Hoszu, Adryel Ginot, Grégory Morilla, Ian Machine Learning Cryptography and Security Distributed, Parallel, and Cluster Computing Algebraic Topology 55N31, 68T05, 94A62, 68W15, 62R40, 68T07, 68T99 68T07, 68W15, 60B99, 94A60 I.2.8; H.1.1 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. |
| title | PTOPOFL: Privacy-Preserving Personalised Federated Learning via Persistent Homology |
| topic | Machine Learning Cryptography and Security Distributed, Parallel, and Cluster Computing Algebraic Topology 55N31, 68T05, 94A62, 68W15, 62R40, 68T07, 68T99 68T07, 68W15, 60B99, 94A60 I.2.8; H.1.1 |
| url | https://arxiv.org/abs/2603.04323 |