Functorial String Diagrams for Reverse-Mode Automatic Differentiation
Functorial String Diagrams for Reverse-Mode Automatic Differentiation
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DOI：
10.4230/lipics.csl.2023.6
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发表时间：
2021-07
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影响因子：
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通讯作者：
Mario Alvarez-Picallo;D. Ghica;David Sprunger;F. Zanasi
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文献类型：
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作者：
Mario Alvarez-Picallo;D. Ghica;David Sprunger;F. Zanasi
我们加强了演算的弦图monoidal类别的层次特征，以捕捉封闭monoidal（和carnival封闭）的结构。使用这种新的语法，我们制定了一个自动微分算法（应用）简单类型的lambda演算的风格[Pearlmutter和Siskind 2008]，我们第一次证明了它的可靠性。为了给出AD算法的有效而有原则的实现，我们定义了一个声音和完整的表示层次字符串图作为一类层次超图，我们称之为超网。
We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.