On Admissible Rank-based Input Normalization Operators

This paper addresses a critical issue in machine learning: the instability of rank-based normalization operators under various transformations. It highlights the shortcomings of existing methods and proposes a new framework based on three axioms to ensure stability and invariance. The work is significant because it provides a formal understanding of the design space for rank-based normalization, which is crucial for building robust and reliable machine learning models.