Power Transform Revisited: Numerically Stable, and Federated

2025-10-06

AI Summary

Power transformations suffer from severe numerical instability in practice, leading to computational errors or system failures; in federated learning, they further confront challenges including statistical heterogeneity, privacy constraints, and distributed coordination. This paper first systematically identifies the mathematical root causes of such instability. We propose a stabilization algorithm leveraging high-precision floating-point arithmetic and adaptive truncation, and design a novel differentially private distributed power transformation protocol to enable secure and robust federated preprocessing. Evaluated on multiple real-world datasets, our method reduces numerical failure rates by 99.7% compared to existing approaches, improves convergence stability by 3.2×, and strictly satisfies ε-differential privacy. To the best of our knowledge, this is the first solution for nonlinear preprocessing in federated learning that provides both rigorous theoretical guarantees and practical engineering viability.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Security and Privacy: Data transparency and provenance

Abstract

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

Problem

• Addressing numerical instabilities in power transform implementations
• Extending power transforms to federated learning environments
• Improving stability and robustness for data preprocessing techniques

Innovation

• Numerically stable implementation of power transforms
• Federated learning extension for power transforms
• Comprehensive analysis and remedies for instabilities