Аннотация
First-order automatic differentiation is a ubiquitous tool across statistics,
machine learning, and computer science. Higher-order implementations of
automatic differentiation, however, have yet to realize the same utility. In
this paper I derive a comprehensive, differential geometric treatment of
automatic differentiation that naturally identifies the higher-order
differential operators amenable to automatic differentiation as well as
explicit procedures that provide a scaffolding for high-performance
implementations.
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