Categorical Foundations

Our Fidelity framework grew from engineering requirements: preserving dimensional meaning through compilation, determining memory placement, and supporting different targets from a shared source. We want an engineer to express a physical operation once and retain its constraints while choosing how it runs.

Categorical deep learning helped us recognize a related problem in model design: connecting a model’s required structure with its parameterized implementation. Our adjoint correspondence entry develops that connection through parameter sharing and differentiation, keeping the laws of each construction explicit.

We are extending this inquiry to the relationships between compilation stages and reasoning modes. A library result should remain usable when its premises hold for the transformed operation. Numeric representation and memory layout add conditions that must be checked at their respective boundaries. Our compilation sheaf design explores how to organize that evidence across the program and its target realizations.