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On the Equivalence of Automatic and Symbolic Differentiation
We show that reverse mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives.
Computing Higher Order Derivatives of Matrix and Tensor Expressions
Optimization is an integral part of most machine learning systems and most numerical optimization schemes rely on the computation of derivatives.
Approximating Concavely Parameterized Optimization Problems
We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy $\varepsilon >0$ by a set of size $O(1/\sqrt{\varepsilon})$.
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