Exploring explainable AI: category theory insights into machine learning algorithms

Explainable artificial intelligence (XAI) is a growing field that aims to increase the transparency and interpretability of machine learning (ML) models. The aim of this work is to use the categorical properties of learning algorithms in conjunction with the categorical perspective of the information in the datasets to give a framework for explainability. In order to achieve this, we are going to define the enriched categories, with decorated morphisms, LearnLearn , ParaPara and MNetMNet of learners, parameterized functions, and neural networks over metric spaces respectively. The main idea is to encode information from the dataset via categorical methods, see how it propagates, and lastly, interpret the results thanks again to categorical (metric) information. This means that we can attach numerical (computable) information via enrichment to the structural information of the category. With this, we can translate theoretical information into parameters that are easily understandable. We will make use of different categories of enrichment to keep track of different kinds of information. That is, to see how differences in attributes of the data are modified by the algorithm to result in differences in the output to achieve better separation. In that way, the categorical framework gives us an algorithm to interpret what the learning algorithm is doing. Furthermore, since it is designed with generality in mind, it should be applicable in various different contexts. There are three main properties of category theory that help with the interpretability of ML models: formality, the existence of universal properties, and compositionality. The last property offers a way to combine smaller, simpler models that are easily understood to build larger ones. This is achieved by formally representing the structure of ML algorithms and information contained in the model. Finally, universal properties are a cornerstone of category theory. They help us characterize an object, not by its attributes, but by how it interacts with other objects. Thus, we can formally characterize an algorithm by how it interacts with the data. The main advantage of the framework is that it can unify under the same language different techniques used in XAI. Thus, using the same language and concepts we can describe a myriad of techniques and properties of ML algorithms, streamlining their explanation and making them easier to generalize and extrapolate.