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.

翻译：联邦学习（FL）面临两个结构性矛盾：梯度共享会引发数据重构攻击，而非独立同分布（non-IID）的客户端分布则会降低聚合质量。本文提出PTOPOFL框架，通过用持续同调（PH）导出的拓扑描述符替代梯度通信，同时应对这两个挑战。客户端仅传输48维的PH特征向量——这是一种紧凑的形状摘要，其多对一结构使得逆向重构在理论上被证明是不适定的——而非模型梯度。服务器执行拓扑引导的个人化聚合：通过客户端PH图之间的Wasserstein相似性进行聚类，对簇内模型进行拓扑加权，并将各簇与全局共识进行融合。我们证明了一个信息压缩定理，表明在强凸损失函数下，PH描述符每样本泄漏的互信息严格少于梯度；同时，我们建立了Wasserstein加权聚合方案的线性收敛性，其误差下界严格小于FedAvg。在非独立同分布的医疗场景（8家医院，其中2家为对抗性）和一个病理性基准测试（10个客户端）中，与FedAvg、FedProx、SCAFFOLD和pFedMe相比，PTOPOFL分别实现了0.841和0.910的AUC值——在两种设置下均为最高——同时将重构风险相对于梯度共享降低了4.5倍。代码公开于https://github.com/MorillaLab/TopoFederatedL，数据公开于https://doi.org/10.5281/zenodo.18827595。