Learning Is a Kan Extension
This provides a foundational theoretical framework for machine learning, potentially impacting all of ML/AI by offering a new perspective on error minimization.
The paper proves that all error minimization algorithms can be expressed as Kan extensions, bridging a gap with prior work that noted similarities between some Kan extensions and machine learning algorithms. This result enables future research into optimizing machine learning by framing algorithms as Kan extensions.
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.