With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support for this types of structure. One approach, due to Abadi and Plotkin, provides a simple differential programming language. Another approach is the notion of a reverse differential category. In the present paper we bring these two approaches together. In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's language, and describe how this categorical model allows one to consider potential improvements to the operational semantics of the language.

中文翻译：

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一种简单的差分编程语言的分类语义

随着对机器学习，尤其是深度学习的兴趣增加，自动微分的使用在计算中变得更加广泛。最近有两项进展为这种类型的结构提供了理论支持。由于Abadi和Plotkin，一种方法提供了一种简单的差分编程语言。另一种方法是反向微分类别的概念。在本文中，我们将这两种方法结合在一起。特别是，我们展示了反向派生类别的扩展如何建模Abadi和Plotkin的语言，并描述了这种分类模型如何使人们可以考虑对语言的操作语义进行潜在的改进。