Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach

Federated learning (FL) has emerged as a powerful paradigm for collaborative model training across distributed clients while preserving data privacy. However, existing FL algorithms predominantly focus on unconstrained optimization problems with exact gradient information, limiting its applicability in scenarios where only noisy function evaluations are accessible or where model parameters are constrained. To address these challenges, we propose a novel zeroth-order projection-based algorithm on Riemannian manifolds for FL. By leveraging the projection operator, we introduce a computationally efficient zeroth-order Riemannian gradient estimator. Unlike existing estimators, ours requires only a simple Euclidean random perturbation, eliminating the need to sample random vectors in the tangent space, thus reducing computational cost. Theoretically, we first prove the approximation properties of the estimator and then establish the sublinear convergence of the proposed algorithm, matching the rate of its first-order counterpart. Numerically, we first assess the efficiency of our estimator using kernel principal component analysis. Furthermore, we apply the proposed algorithm to two real-world scenarios: zeroth-order attacks on deep neural networks and low-rank neural network training to validate the theoretical findings.

Interpretable Hybrid-Rule Temporal Point Processes

Temporal Point Processes (TPPs) are widely used for modeling event sequences in various medical domains, such as disease onset prediction, progression analysis, and clinical decision support. Although TPPs effectively capture temporal dynamics, their lack of interpretability remains a critical challenge. Recent advancements have introduced interpretable TPPs. However, these methods fail to incorporate numerical features, thereby limiting their ability to generate precise predictions. To address this issue, we propose Hybrid-Rule Temporal Point Processes (HRTPP), a novel framework that integrates temporal logic rules with numerical features, improving both interpretability and predictive accuracy in event modeling. HRTPP comprises three key components: basic intensity for intrinsic event likelihood, rule-based intensity for structured temporal dependencies, and numerical feature intensity for dynamic probability modulation. To effectively discover valid rules, we introduce a two-phase rule mining strategy with Bayesian optimization. To evaluate our method, we establish a multi-criteria assessment framework, incorporating rule validity, model fitting, and temporal predictive accuracy. Experimental results on real-world medical datasets demonstrate that HRTPP outperforms state-of-the-art interpretable TPPs in terms of predictive performance and clinical interpretability. In case studies, the rules extracted by HRTPP explain the disease progression, offering valuable contributions to medical diagnosis.