Ian Morilla

Kelly L Vomo-Donfack, Adryel Hoszu, Grégory Ginot et al.

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.

Mariem Abaach, Ian Morilla

A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both conventional and deep learning models. We introduce GeoTop, a mathematically principled framework that unifies Topological Data Analysis (TDA) and Lipschitz-Killing Curvatures (LKCs) to resolve this ambiguity. Unlike hybrid deep learning approaches, GeoTop provides intrinsic interpretability by fusing the capacity of persistent homology to identify robust topological signatures with the precision of LKCs in quantifying local geometric features such as boundary complexity and surface regularity. The framework's clinical utility is demonstrated through its application to skin lesion classification, where it achieves a consistent accuracy improvement of 3.6% and reduces false positives and negatives by 15-18% compared to conventional single-modality methods. Crucially, GeoTop directly addresses the problem of topological equivalence by incorporating geometric differentiators, providing both theoretical guarantees (via a formal lemma) and empirical validation via controlled benchmarks. Beyond its predictive performance, GeoTop offers inherent mathematical interpretability through persistence diagrams and curvature-based descriptors, computational efficiency for large datasets (processing 224x224 pixel images in less or equal 0.5 s), and demonstrated generalisability to molecular-level data. By unifying topological invariance with geometric sensitivity, GeoTop provides a principled, interpretable solution for advanced shape discrimination in diagnostic imaging.