用范畴论构建更鲁棒的机器学习模型
Symmetry-Enriched Learning: A Category-Theoretic Framework for Robust Machine Learning Models
- 用高阶对称性与范畴论设计新型学习模型
- 理论证明其提升模型泛化与收敛性
- 适合数学严谨性要求高的研究者
本文提出一种融合高阶对称性与范畴论的新型机器学习框架。引入超对称范畴和函子表示等新数学结构，用于建模学习算法中的复杂变换。贡献包括对称性增强学习模型的设计、基于范畴对称性的优化技术开发，以及对模型鲁棒性、泛化能力与收敛性的理论分析。通过严格证明与实际应用，验证了高维范畴结构能同时强化现代机器学习算法的理论基础与实践性能，为研究与创新开辟新方向。
原文摘要 · Abstract (English)
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to model complex transformations within learning algorithms. Our contributions include the design of symmetry-enriched learning models, the development of advanced optimization techniques leveraging categorical symmetries, and the theoretical analysis of their implications for model robustness, generalization, and convergence. Through rigorous proofs and practical applications, we demonstrate that incorporating higher-dimensional categorical structures enhances both the theoretical foundations and practical capabilities of modern machine learning algorithms, opening new directions for research and innovation.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。