A Geometric Theory of Higher-Order Automatic Differentiation
Computation
2019-01-01 v1
Abstract
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.
Cite
@article{arxiv.1812.11592,
title = {A Geometric Theory of Higher-Order Automatic Differentiation},
author = {Michael Betancourt},
journal= {arXiv preprint arXiv:1812.11592},
year = {2019}
}
Comments
55 pages, 10 figures