# Learning Is a Kan Extension

arXiv: https://arxiv.org/abs/2502.13810 · HTML: https://mlsanity.com/paper/2502.13810/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 10 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Builds on (most cited first, 2 of 2)

- [Kan Extensions in Data Science and Machine Learning](https://mlsanity.com/paper/2203.09018/) (2022)
- [Fast Left Kan Extensions Using The Chase](https://mlsanity.com/paper/2205.02425/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning Transfers: Kan Extensions of Topological Invariants of Learned Representations](https://mlsanity.com/paper/2606.07627/) (2026)

## Abstract (arXiv)

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.