Adaptive Multi-Scale Fourier Neural Operator Learning with Manifold-Preserving Local Density Oversampling for Coarse-Grained Wi-Fi CSI-Based Human Activity Recognition

Wi-Fi Channel State Information (CSI) provides a privacy-preserving modality for human activity recognition (HAR), particularly in environments where activity classes vary in complexity and temporal scale. This work presents an integrated framework that combines multi-scale Fourier operator learning with manifold-aware density refinement for coarse-grained CSI-based HAR. The adaptive Multi-Scale Fourier Neural Operator (MS-FNO) models CSI trajectories as structured stochastic processes and learns activity mappings directly in the function space. Its multi-scale design enables the model to capture both simple, quasi-periodic macro-activities and more complex multi-person interactions by adjusting its receptive field according to the intrinsic structure of each activity class. To address class imbalance and representation collapse, the framework incorporates a Manifold-Preserving Local Density Oversampling (MPLDO) module that performs locality-constrained interpolation in a correlation-projected latent subspace, followed by classifier-guided pruning to maintain decision-boundary consistency. Experimental results show that the combined MS-FNO and MPLDO pipeline improves class-conditional separability and enhances recognition accuracy across both low-complexity and high-complexity activities. The findings highlight the effectiveness of this integrated operator-learning pipeline for privacy-aware activity monitoring in cafés, elder-care facilities, hospitals, and other real-world environments where coarse-to-complex activity understanding is required.