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The Elements of Differentiable Programming

Created by
  • Haebom

Author

Mathieu Blondel, Vincent Roulet

Outline

This paper comprehensively reviews the fundamental concepts of differentiable programming. Focusing on the recent advances in artificial intelligence, including large-scale models, massive datasets, high-performance hardware, and the transformative power of differentiable programming, we introduce differentiable programming, a new programming paradigm that enables end-to-end differentiation of complex computer programs (including control flow and data structures). Drawing on several areas of computer science and applied mathematics, including automatic differentiation, graphical models, optimization, and statistics, we adopt two major perspectives, optimization and probability, and present a clear analogy between the two perspectives. Beyond simply differentiating programs, we emphasize the thoughtful design of programs for differentiation, and by making programs differentiable, we provide a method for quantifying the uncertainty associated with the program output by introducing a probability distribution over the program execution.

Takeaways, Limitations

Takeaways: Systematically organizes the basic concepts of differentiable programming, providing a theoretical foundation for researchers in related fields. It improves understanding by presenting two perspectives, optimization and probability, in an integrated manner. It presents a new approach to quantifying uncertainty through the differentiability of programs.
Limitations: Lack of detailed descriptions of specific algorithms or application cases. Lack of discussion of the limitations of differentiable programming or problems that may arise in practical applications. Lack of discussion of the level of support for various programming languages or frameworks.
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