Token Space: A Category Theory Framework for AI Computations
Wuming Pan
This paper introduces the Token Space framework, a novel mathematical
construct designed to enhance the interpretability and effectiveness of deep
learning models through the application of category theory. By establishing a
categorical structure at the Token level, we provide a new lens through which
AI computations can be understood, emphasizing the relationships between
tokens, such as grouping, order, and parameter types. We explore the
foundational methodologies of the Token Space, detailing its construction, the
role of construction operators and initial categories, and its application in
analyzing deep learning models, specifically focusing on attention mechanisms
and Transformer architectures. The integration of category theory into AI
research offers a unified framework to describe and analyze computational
structures, enabling new research paths and development possibilities. Our
investigation reveals that the Token Space framework not only facilitates a
deeper theoretical understanding of deep learning models but also opens avenues
for the design of more efficient, interpretable, and innovative models,
illustrating the significant role of category theory in advancing computational
models.