derivativesremain

Derivativesremain is a term used in discussions of differentiable systems to denote the persistence and accessibility of derivative information through transformations, optimizations, or code generation. It is not an established, universally defined term, but a label used in some communities to express a design goal or mathematical observation.

In mathematics, derivativesremain can refer to the compatibility of derivatives under composition. If g = f ∘ h and certain regularity conditions hold, the chain rule relates Dg to f' and Dh, illustrating how derivative structure can remain coherent under function composition.

In computation and automatic differentiation, derivativesremain describes a property of software tools and compilers: after transformations such as inlining, loop fusion, or vectorization, derivative information (gradients, Jacobians) remains available, correctly aligned with the transformed program.

Typical uses include differentiable programming, optimization, and simulation workflows where gradient accuracy and accessibility must be preserved despite program rewrites.

Limitations include lack of formal definition, context sensitivity, and potential trade-offs with performance or numerical stability. As a term, it serves as a heuristic or design principle rather than a universal standard.