所有误差最小化算法均可看作范畴论中的肯扩展，为优化机器学习提供新视角。
Learning Is a Kan Extension
- 用范畴论的肯扩展统一描述各类误差最小化算法
- 揭示误差源于数据在损毁与无损变换中的表现差异
- 适合对数学基础或算法本质感兴趣的研究者
先前研究已证明高效计算肯扩展的算法存在，且某些肯扩展与机器学习算法有有趣相似性。本文填补空白，证明所有误差最小化算法均可表示为肯扩展。该结果为未来通过肯扩展形式研究机器学习算法优化奠定基础。此表示的一个推论是从损毁与无损数据变换的角度重新呈现误差。
原文摘要 · Abstract (English)
Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all error minimisation algorithms may be presented as a Kan extension. This result provides a foundation for future work to investigate the optimisation of machine learning algorithms through their presentation as Kan extensions. A corollary of this representation of error-minimising algorithms is a presentation of error from the perspective of lossy and lossless transformations of data.
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