Clone-Resistant Weights in Metric Spaces: A Framework for Handling Redundancy Bias

2025-02-05

AI Summary

In metric spaces, adversarial cloning of elements can induce weighted distortions, compromising robustness in aggregation tasks. Method: We propose the first formal “cloning-immune” robust weighting framework. Our approach generalizes the Maximum Uncertainty Principle to arbitrary metric spaces; establishes a three-axiom system—symmetry, continuity, and cloning immunity; and proves axiom compatibility and solution existence rigorously in Euclidean space, accompanied by a computationally tractable construction algorithm. Contributions: (i) Theoretically, we establish the axiomatic foundation and existence guarantee for cloning-immune weights; (ii) Methodologically, we generalize robust weighting from discrete voting settings to continuous metric spaces; (iii) Practically, our framework supports robust domain adaptation, construction of multi-task benchmarks, and manipulation-resistant voting-based recommendation systems.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations? This problem arises in various contexts. For instance, the elements could represent data points, requiring robust domain adaptation. Alternatively, they might represent tasks to be aggregated into a benchmark; or questions about personal political opinions in voting advice applications. This article introduces a theoretical framework for dealing with such problems. We propose clone-proof representation functions as a solution concept. These functions distribute importance across elements of a set such that similar objects (``clones'') share (some of) their weights, thus avoiding a potential bias introduced by their multiplicity. Our framework extends the maximum uncertainty principle to accommodate general metric spaces and includes a set of axioms - symmetry, continuity, and clone-proofness - that guide the construction of representation functions. Finally, we address the existence of representation functions satisfying our axioms in the significant case of Euclidean spaces and propose a general method for their construction.

Problem

• Handling redundancy bias in metric spaces
• Weighing elements resistant to adversarial manipulations
• Clone-proof representation functions for fair importance distribution

Innovation

• Clone-proof representation functions
• Maximum uncertainty principle extension
• Axiom-guided function construction