Combinatory Adjoints and Differentiation. (arXiv:2207.00847v1 [cs.PL])

We develop a compositional approach for automatic and symbolic
differentiation based on categorical constructions in functional analysis where
derivatives are linear functions on abstract vectors rather than being limited
to scalars, vectors, matrices or tensors represented as multi-dimensional
arrays. We show that both symbolic and automatic differentiation can be
performed using a differential calculus for generating linear functions
representing Fr\'echet derivatives based on rules for primitive, constant,
linear and bilinear functions as well as their sequential and parallel
composition. Linear …

arxiv differentiation pl