Learning Is a Kan Extension

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.

Using Enriched Category Theory to Construct the Nearest Neighbour Classification Algorithm

Exploring whether Enriched Category Theory could provide the foundation of an alternative approach to Machine Learning. This paper is the first to construct and motivate a Machine Learning algorithm solely with Enriched Category Theory. In order to supplement evidence that Category Theory can be used to motivate robust and explainable algorithms, it is shown that a series of reasonable assumptions about a dataset lead to the construction of the Nearest Neighbours Algorithm. In particular, as an extension of the original dataset using profunctors in the category of Lawvere metric spaces. This leads to a definition of an Enriched Nearest Neighbours Algorithm, which consequently also produces an enriched form of the Voronoi diagram. This paper is intended to be accessible without any knowledge of Category Theory

Two Novel Performance Improvements for Evolving CNN Topologies

Convolutional Neural Networks (CNNs) are the state-of-the-art algorithms for the processing of images. However the configuration and training of these networks is a complex task requiring deep domain knowledge, experience and much trial and error. Using genetic algorithms, competitive CNN topologies for image recognition can be produced for any specific purpose, however in previous work this has come at high computational cost. In this work two novel approaches are presented to the utilisation of these algorithms, effective in reducing complexity and training time by nearly 20%. This is accomplished via regularisation directly on training time, and the use of partial training to enable early ranking of individual architectures. Both approaches are validated on the benchmark CIFAR10 data set, and maintain accuracy.