SSRN Author: Henri-Olivier DucheHenri-Olivier Duche SSRN Content
http://www.ssrn.com/author=1384187
http://www.ssrn.com/rss/en-usTue, 28 Nov 2017 07:23:16 GMTeditor@ssrn.com (Editor)Tue, 28 Nov 2017 07:23:16 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Coarse Grain Automatic Differentiation: A Practical Approach to Fast and Exact Computation of First and Second Order Derivatives in SoftwareThe evaluations done by a program at runtime can be modeled by computational Directed Acyclic Graphs (DAGs) at various abstraction levels.
Applying the multivariate chain rule on those computational DAGs enables the automation of total derivatives computation, which is exploited at a fine-grain level by Automatic Differentiation (AD).
Coarse Grain Automatic Differentiation (CGAD) is a framework that exploits this principle at a higher level, leveraging on software domain model.
All nodes in the computational DAG are responsible for computing local partial derivatives with respect to their direct dependencies while the CGAD framework is responsible for composing them into first and second order total derivatives.
This separation of concerns between local and global computations offers several key software engineering advantages:
It eases integration, makes the system decoupled and inherently extensible and allows hybrid differentiation (i.e. connecting derivatives from different ...
http://www.ssrn.com/abstract=2913627
http://www.ssrn.com/1646174.htmlMon, 27 Nov 2017 15:23:24 GMTREVISION: Second Order Differentiation Formula in a Computational GraphF. L. Bauer expressed a first order differentiation closed formula in a computational graph based on the multivariate chain rule. We propose and prove in this article a similarly closed formula for second order derivative.
We analyse the complexity of those two formulas and prove that, in certain cases, it is exponential with respect to the number of vertices in the computational graph.
http://www.ssrn.com/abstract=2905103
http://www.ssrn.com/1645585.htmlFri, 24 Nov 2017 10:44:01 GMTREVISION: Coarse Grain Automatic Differentiation: A Practical Approach to Fast and Exact Computation of First and Second Order Derivatives in SoftwareCoarse Grain Automatic Differentiation automatically computes first and second order total derivatives in software by applying the multivariate chain rule at any abstraction level. The choice of abstraction level is a trade-off between speed and mathematical complexity.
In this paper we describe a very appealing way for the software industry to strike the appropriate abstraction level by leveraging software modularity.
All modules are responsible for computing local partial derivatives with respect to their direct dependencies.
The encapsulation of local partial derivative computation methods allows hybrid differentiation that bridges the gap between software engineering concerns (integrability, maintainability) and differentiation concerns (speed, exactness).
The modules can take advantage of mathematical simplifications, the implicit function theorem, and local computation reuses to significantly speed up total derivatives propagation.
Finally, we give a ...
http://www.ssrn.com/abstract=2913627
http://www.ssrn.com/1565584.htmlFri, 10 Feb 2017 13:15:55 GMTREVISION: Coarse Grain Automatic Differentiation: A Practical Approach to Fast and Exact Computation of First and Second Order Derivatives in SoftwareCoarse Grain Automatic Differentiation automatically computes first and second order total derivatives in software by applying the multivariate chain rule at any abstraction level. The choice of abstraction level is a trade-off between speed and mathematical complexity.
In this paper we describe a very appealing way for the software industry to strike the appropriate abstraction level by leveraging software modularity.
All modules are responsible for computing local partial derivatives with respect to their direct dependencies.
The encapsulation of local partial derivative computation methods allows hybrid differentiation that bridges the gap between software engineering concerns (integrability, maintainability) and differentiation concerns (speed, exactness).
The modules can take advantage of mathematical simplifications, the implicit function theorem, and local computation reuses to significantly speed up total derivatives propagation.
Finally, we give a ...
http://www.ssrn.com/abstract=2913627
http://www.ssrn.com/1565044.htmlThu, 09 Feb 2017 07:24:51 GMTREVISION: Second Order Differentiation Formula in a Computational GraphF.L. Bauer expressed a first order differentiation closed formula in a computational graph based on the first order multivariate chain rule. We propose and prove in this article a similarly closed formula valid for the second order derivative in a computational graph based on the second order multivariate chain rule.
http://www.ssrn.com/abstract=2905103
http://www.ssrn.com/1560732.htmlWed, 25 Jan 2017 00:56:55 GMT