A Mathematical Theory of GPU Layouts: Applying Category Theory and Operads
2025-09-25
This paper introduces CuTe, a novel approach to GPU memory layouts, and delves into the underlying mathematical theory. CuTe layouts leverage category theory and operads, employing diagrammatic computation and standard representations to solve the problem of mapping multi-dimensional data to one-dimensional GPU memory. This provides a theoretical foundation for optimizing memory access patterns and utilizing specialized hardware instructions like tensor cores. The paper focuses on the concept of tractable layouts, layout functions, and layout operations such as coalesce, complement, and composition, demonstrating how a category-theoretic framework efficiently computes layout composition.
Read more
Development