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The com- bination of combinatory differentiation and computing formal adjoints turns out to be behaviorally equivalent to reverse-mode automatic differentiation. In particular, it provides opportunities for opti- mizations where matrices are too inefficient to represent linear functions.
Jul 2, 2022 · We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis.
Adjoint of linear map expressed as matrix is its transpose: (M?) ∗. = (MT ?). Standard approach: Represent linear maps as matrices.
We provide an adjoint calculus for symbolically calculating the adjoints of linear functions in combinatory form. We identify relational reduction and tensor ...
The combination of combinatory differentiation and computing formal adjoints turns out to be behaviorally equivalent to reverse-mode automatic differentiation.
Duration: 29:42
Posted: Apr 5, 2022
Posted: Apr 5, 2022
Combinatory Adjoints and Differentiation · List of references · Publications that cite this publication.
Abstract. Various algorithmic differentiation tools have been developed and applied to large-scale simulation software for physical phenomena.
As a direct consequence of the Kan Extension Theorem, the derivative functor, D, on (combinatorial) species, has both a left adjoint, MX, ...
This implementation of combinatory AD is a standalone tool, which provides for both forward-mode AD (FAD) and reverse-mode AD (RAD).