用特征函数距离实现公平分类，稳定高效且不降精度。

Fair classification is a critical challenge that has gained increasing importance due to international regulations and its growing use in high-stakes decision-making settings. Existing methods often rely on adversarial learning or distribution matching across sensitive groups; however, adversarial learning can be unstable, and distribution matching can be computationally intensive. To address these limitations, we propose a novel approach based on the characteristic function distance. Our method ensures that the learned representation contains minimal sensitive information while maintaining high effectiveness for downstream tasks. By utilizing characteristic functions, we achieve a more stable and efficient solution compared to traditional methods. Additionally, we introduce a simple relaxation of the objective function that guarantees fairness in common classification models with no performance degradation. Experimental results on benchmark datasets demonstrate that our approach consistently matches or achieves better fairness and predictive accuracy than existing methods. Moreover, our method maintains robustness and computational efficiency, making it a practical solution for real-world applications.