Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings

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 $ Ł_{T} $ and $ ¶_{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 $ ¶_{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 $ \Emb $, accompanied by the concept of divergence as a decoration on $ \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.