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| Main Authors: | , |
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| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17823224 |
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Table of Contents:
- The rapid proliferation of Artificial Intelligence (AI) systems across critical domains necessitates a principled approach to their design, ensuring not only high performance but also adherence to predefined norms for robustness and alignment. This paper introduces a framework for the normative engineering of AI, specifically leveraging the elegant and powerful mathematical structures of inner product geometry. We propose that by conceptualizing AI system states, data representations, and decision boundaries within suitable inner product spaces, we can formulate and enforce explicit geometric constraints that directly translate into improved adversarial robustness and enhanced alignment with human values and intentions. We explore how notions of distance, angle, and projection within these spaces can be utilized to quantify deviation from desired behaviors and to regularize learning processes. For robustness, inner product geometry offers avenues for defining safety margins around decision boundaries and for projecting adversarial perturbations into benign subspaces. For alignment, it provides mechanisms to embed ethical principles as "norm vectors" or "subspaces" and to optimize models to maintain geometric proximity or orthogonality to these representations. This approach offers a unified, mathematically rigorous paradigm for building trustworthy AI, moving beyond ad-hoc solutions towards a systematic integration of normative considerations into the core engineering process. We discuss the theoretical foundations, potential methodological implications, and the challenges and future directions for this geometric perspective on AI safety and ethics.