Elimination Techniques for Cheap Jacobians
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The generation of optimized code for evaluating the Jacobian matrix of a vector function is known to result in a remarkable speedup of three and more compared to standard methods of Automatic Differentiation in most cases. So far, this optimization has been built on the elimination of vertices in the computational graph. We show that vertex elimination in general does not lead to optimal Jacobian code. We introduce two new elimination methods and demonstrate their superiority over the vertex elimination approach.
KeywordsVector Function Scalar Multiplication Computational Graph Edge Label Automatic Differentiation
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