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CityAD, an Automatic Differentiation package

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CityAD Fall 2020

Automatic Differentiation, or Algorithmic Differentiation, is a term used to describe a collection of techniques that can be used to calculate the derivatives of complicated functions. Because derivatives play a key role in computational analyses, statistics, and machine and deep learning algorithms, the ability to quickly and efficiently take derivatives is a crucial one. Other methods for taking derivatives, however, including Finite Differentiation and Symbolic Differentiation have drawbacks, including extreme slowness, precision errors, inaccurate in high dimensions, and memory intensivity. Automatic differentiation addresses many of these concerns by providing an exact, high-speed, and highly-applicable method to calculate derivatives. Its importance is evidenced by the fact that it is used as a backbone for TensorFlow, one of the most widely-used machine learning libraries. In this project, we will be implementing an Automatic Differentiation library that can be used as the basis for analysis methods, including a Newton’s Method extension that we will illustrate.

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