Eigen-AD: Algorithmic Differentiation of the Eigen Library

TL;DR

Eigen-AD introduces enhancements for applying Algorithmic Differentiation to the Eigen linear algebra library, including performance optimizations and symbolic derivative calculations, validated through benchmarks with the dco/c++ tool.

Contribution

It provides a modular approach to integrate symbolic derivatives and optimize AD performance in Eigen using add-on modules, advancing AD application in linear algebra.

Findings

Significant performance improvements demonstrated in benchmarks

Enhanced handling of expression templates for better efficiency

Successful integration of symbolic derivatives for core Eigen operations

Abstract

In this work we present useful techniques and possible enhancements when applying an Algorithmic Differentiation (AD) tool to the linear algebra library Eigen using our in-house AD by overloading (AD-O) tool dco/c++ as a case study. After outlining performance and feasibility issues when calculating derivatives for the official Eigen release, we propose Eigen-AD, which enables different optimization options for an AD-O tool by providing add-on modules for Eigen. The range of features includes a better handling of expression templates for general performance improvements, as well as implementations of symbolically derived expressions for calculating derivatives of certain core operations. The software design allows an AD-O tool to provide specializations to automatically include symbolic operations and thereby keep the look and feel of plain AD by overloading. As a showcase, dco/c++ is provided with such a module and its significant performance improvements are validated by benchmarks.