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Automatic Functional Differentiation in JAX

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arxiv 2311.18727 v2 pith:RJLFBAIJ submitted 2023-11-30 cs.PL cs.CLcs.LG

Min Lin This is my paper
classification cs.PLcs.CLcs.LG
keywords functionsfunctionaldifferentiationprimitiveautomaticfunctionalshigher-orderimplement
verification ladder T0 review T1 audit T2 compute T3 formal
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We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

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Cited by 2 Pith papers

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