On Admissible Rank-based Input Normalization Operators
Published:Dec 27, 2025 13:28
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Identifies instability issues in existing rank-based normalization methods.
- •Proposes three axioms for designing stable and invariant rank-based normalization operators.
- •Provides a formal framework for understanding the design space of valid operators.
- •Highlights the importance of feature-wise rank representation and monotone, Lipschitz-continuous scalarization.
Reference
“The paper proposes three axioms that formalize the minimal invariance and stability properties required of rank-based input normalization.”