Learning with p-adic Numbers: A Novel Approach to Machine Learning
Research Paper#Machine Learning, p-adic Numbers, Representation Learning🔬 Research|Analyzed: Jan 3, 2026 19:44•
Published: Dec 27, 2025 19:40
•1 min read
•ArXivAnalysis
This paper explores the use of p-adic numbers, a non-Archimedean field, as an alternative to real numbers in machine learning. It challenges the conventional reliance on real-valued representations and Euclidean geometry, proposing a framework based on the hierarchical structure of p-adic numbers. The work is significant because it opens up a new avenue for representation learning, potentially offering advantages in areas like code theory and hierarchical data modeling. The paper's theoretical exploration and the demonstration of representing semantic networks highlight its potential impact.
Key Takeaways
- •Proposes a novel machine learning framework using p-adic numbers instead of real numbers.
- •Explores the potential of p-adic numbers for hierarchical representation learning and code theory.
- •Provides theoretical foundations and algorithms for classification, regression, and representation learning within the p-adic framework.
- •Demonstrates the representation of semantic networks using p-adic linear networks, a construction not possible with real numbers.
- •Identifies open problems and opportunities for future research in this new framework.
Reference / Citation
View Original"The paper establishes the building blocks for classification, regression, and representation learning with the $p$-adics, providing learning models and algorithms."