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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.17816006 |
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Table of Contents:
- The relentless pursuit of artificial intelligence (AI) advancements necessitates increasingly efficient and robust optimization strategies. Traditional optimization algorithms, while powerful, are often hand-designed and require significant hyperparameter tuning for diverse tasks. This paper introduces "Meta-Calculus," a novel paradigm that conceptualizes the very rules of optimization, including differentiation and update mechanisms, as learnable entities within a meta-learning framework. By enabling AI systems to learn and adapt their own optimization principles, Meta-Calculus aims to transcend the limitations of fixed, human-engineered optimizers. We propose a methodology where optimization rules are parameterized by neural networks, allowing for end-to-end differentiable learning of these meta-rules. This framework offers the potential for faster convergence, improved generalization across a spectrum of tasks, and enhanced adaptability to novel problem settings. We delve into the theoretical underpinnings, discuss its distinction from existing meta-optimization and automatic differentiation techniques, and explore its implications for creating more autonomous and intelligent AI systems. Experimental results, hypothesized from the theoretical framework, demonstrate how Meta-Calculus can discover highly efficient and specialized optimization routines, leading to superior performance in complex, high-dimensional spaces, and mitigating common issues like saddle points and vanishing gradients more effectively than traditional methods. The discussion covers the advantages, computational challenges, and future research directions of this ambitious approach, positioning Meta-Calculus as a foundational step towards truly adaptive and self-improving AI.