Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings

Abstract

The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$ and $\mathcal{P}_T$, providing schematic representations of the semantics of a text $ T $, and reframing the selection of the element with maximum probability as a categorical notion. Additionally, the monoidal category $\mathcal{P}_T$ is constructed to visualize various methods of extracting semantic information from $T$, offering a dimension-agnostic definition of semantic spaces reliant solely on information within the text. Furthermore, the paper defines the categories of configurations Conf and word embeddings $\mathcal{Emb}$, accompanied by the concept of divergence as a decoration on $\mathcal{Emb}$. It establishes a mathematically precise method for comparing word embeddings, demonstrating the equivalence between the GloVe and Word2Vec algorithms and the metric MDS algorithm, transitioning from neural network algorithms (black box) to a transparent framework. Finally, the paper presents a mathematical approach to computing biases before embedding and offers insights on mitigating biases at the semantic space level, advancing the field of explainable artificial intelligence.