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On the Equivalence of Automatic and Symbolic Differentiation

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abstract

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. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that symbolic differentiation suffers from "expression swell" whereas automatic differentiation does not. Here, we show that this statement is not true. "Expression swell" refers to the phenomenon of a much larger representation of the derivative as opposed to the representation of the original function.

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math.OC 1

years

2025 1

verdicts

CONDITIONAL 1

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  • Information Preserving Line Search via Bayesian Optimization math.OC · 2025-07-21 · conditional · none · ref 20 · internal anchor

    A Bayesian-optimization-based line search that keeps all past evaluations chooses step lengths and is claimed to converge with fewer function evaluations on CUTEst benchmarks.