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Distributions for Compositionally Differentiating Parametric Discontinuities
Jesse Michel · Kevin Mu · Xuanda Yang · Sai Praveen Bangaru · Elias Rojas Collins · Gilbert Bernstein · Jonathan Ragan-Kelley · Michael Carbin · Tzu-Mao Li

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in Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators »
Event URL: https://openreview.net/forum?id=VVqt0MThMd »

Computations in computer graphics, robotics, and probabilistic inference often require differentiating integrals with discontinuous integrands. Popular differentiable programming languages do not support the differentiation of these integrals. To address this problem, we extend distribution theory to provide semantic definitions for a broad class of programs in a programming language, Potto. Potto can differentiate parametric discontinuities under integration, and it also supports first-order functions and compositional evaluation. We formalize the meaning of programs using denotational semantics and the evaluation of programs using operational semantics. We prove correctness theorems about the semantics and prove that the operational semantics are compositional, enabling separate compilation of programs and overcoming compile-time bottlenecks. Using Potto, we implement a prototype differentiable renderer with separately compiled shaders.

Author Information

Jesse Michel (Computer Science and Artificial Intelligence Laboratory, Electrical Engineering & Computer Science)
Kevin Mu
Xuanda Yang (Zhejiang University)
Sai Praveen Bangaru (Massachusetts Institute of Technology)
Elias Rojas Collins (Massachusetts Institute of Technology)
Gilbert Bernstein
Jonathan Ragan-Kelley (Massachusetts Institute of Technology)
Michael Carbin (MIT)
Tzu-Mao Li (University of California, San Diego)

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