Permutation-Invariant Representation Learning for Robust and Privacy-Preserving Feature Selection

Feature selection eliminates redundancy among features to improve downstream task performance while reducing computational overhead. Existing methods often struggle to capture intricate feature interactions and adapt across diverse application scenarios. Recent advances employ generative intelligence to alleviate these drawbacks. However, these methods remain constrained by permutation sensitivity in embedding and reliance on convexity assumptions in gradient-based search. To address these limitations, our initial work introduces a novel framework that integrates permutation-invariant embedding with policy-guided search. Although effective, it still left opportunities to adapt to realistic distributed scenarios. In practice, data across local clients is highly imbalanced, heterogeneous and constrained by strict privacy regulations, limiting direct sharing. These challenges highlight the need for a framework that can integrate feature selection knowledge across clients without exposing sensitive information. In this extended journal version, we advance the framework from two perspectives: 1) developing a privacy-preserving knowledge fusion strategy to derive a unified representation space without sharing sensitive raw data. 2) incorporating a sample-aware weighting strategy to address distributional imbalance among heterogeneous local clients. Extensive experiments validate the effectiveness, robustness, and efficiency of our framework. The results further demonstrate its strong generalization ability in federated learning scenarios. The code and data are publicly available: https://anonymous.4open.science/r/FedCAPS-08BF.