%0 Journal Article %1 betancourt2018geometric %A Betancourt, Michael %D 2018 %K autograd geometry %T A Geometric Theory of Higher-Order Automatic Differentiation %U http://arxiv.org/abs/1812.11592 %X 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.

@article{betancourt2018geometric, 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.}, added-at = {2019-07-20T20:34:22.000+0200}, author = {Betancourt, Michael}, biburl = {https://www.bibsonomy.org/bibtex/29d3917cd4ae025be58b1bb43378b8358/kirk86}, description = {[1812.11592] A Geometric Theory of Higher-Order Automatic Differentiation}, interhash = {529f9bac377386cf4484633fcb336773}, intrahash = {9d3917cd4ae025be58b1bb43378b8358}, keywords = {autograd geometry}, note = {cite arxiv:1812.11592Comment: 55 pages, 10 figures}, timestamp = {2019-07-20T20:34:22.000+0200}, title = {A Geometric Theory of Higher-Order Automatic Differentiation}, url = {http://arxiv.org/abs/1812.11592}, year = 2018 }