Learning Is a Kan Extension

TL;DR

This paper proves that all error minimisation algorithms in machine learning can be represented as Kan extensions, establishing a theoretical foundation for optimizing algorithms via categorical structures.

Contribution

It demonstrates that error minimisation algorithms are fundamentally expressible as Kan extensions, bridging category theory and machine learning optimization.

Findings

All error minimisation algorithms can be represented as Kan extensions.

Provides a categorical foundation for analyzing machine learning algorithms.

Links error analysis to data transformations in a formal framework.

Abstract

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.