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.
翻译：我们发现,反向模式自动区分和象征性区分等同,即两者在计算衍生物时都执行相同的操作,这与它们大相径庭的共同主张形成鲜明对照。 其区别往往表现为声称象征性区别有“表情膨胀”,而自动区分则没有。 我们在这里表明,这一说法是不真实的。 “表情膨胀”是指衍生物代表比最初功能代表大得多的现象。
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