FedRMamba: Federated Residual Mamba for Multivariate Time-Series Forecasting

Time series forecasting underpins many real-world services. Recent trends have focused on foundation models inspired by the paradigm of large language models, which rely on large volumes of centralized time-series data across diverse domains. However, such approaches raise significant concerns regarding data privacy. Federated learning (FL) has emerged as a promising paradigm for training unified time-series models using isolated datasets distributed across multiple clients. Nevertheless, existing FL methods face two critical challenges: heterogeneous variables and heterogeneous temporal correlations. To address these issues, we propose FedRMamba, a personalized federated forecasting framework built entirely from Mamba state-space blocks. Each client adopts a residual-coupled architecture, where a global frequency-aware Mamba module captures the common low-frequency structures shared across different variables, while a local patch-wise Mamba module learns personalized high-frequency patterns within the multivariate context. To clearly separate these responsibilities, we introduce a frequency-aware supervision that aligns the global path with low-frequency components and the local path with high-frequency residuals. Additionally, we design a gated fusion mechanism that dynamically combines the low-frequency and high-frequency components for improved prediction. We conduct extensive experiments to evaluate the performance of our proposed framework, demonstrating its effectiveness in handling heterogeneous data in federated settings.