Distributions for Compositionally Differentiating Parametric Discontinuities
Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities du...
| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Association for Computing Machinery
2024
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| Online Access: | https://hdl.handle.net/1721.1/154393 |
| _version_ | 1811080470201368576 |
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| author | Michel, Jesse Mu, Kevin Yang, Xuanda Bangaru, Sai Praveen Collins, Elias Rojas Bernstein, Gilbert Ragan-Kelley, Jonathan Carbin, Michael Li, Tzu-Mao |
| author_facet | Michel, Jesse Mu, Kevin Yang, Xuanda Bangaru, Sai Praveen Collins, Elias Rojas Bernstein, Gilbert Ragan-Kelley, Jonathan Carbin, Michael Li, Tzu-Mao |
| author_sort | Michel, Jesse |
| collection | MIT |
| description | Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities during differentiation. This is incorrect for
<jats:italic>parametric discontinuities</jats:italic>
—conditionals containing at least one real-valued parameter and at least one variable of integration. We introduce Potto, the first differentiable first-order programming language to soundly differentiate parametric discontinuities. We present a denotational semantics for programs and program derivatives and show the two accord. We describe the implementation of Potto, which enables separate compilation of programs. Our prototype implementation overcomes previous compile-time bottlenecks achieving an 88.1x and 441.2x speed up in compile time and a 2.5x and 7.9x speed up in runtime, respectively, on two increasingly large image stylization benchmarks. We showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders. |
| first_indexed | 2024-09-23T11:32:12Z |
| format | Article |
| id | mit-1721.1/154393 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:32:12Z |
| publishDate | 2024 |
| publisher | Association for Computing Machinery |
| record_format | dspace |
| spelling | mit-1721.1/1543932024-09-19T05:48:04Z Distributions for Compositionally Differentiating Parametric Discontinuities Michel, Jesse Mu, Kevin Yang, Xuanda Bangaru, Sai Praveen Collins, Elias Rojas Bernstein, Gilbert Ragan-Kelley, Jonathan Carbin, Michael Li, Tzu-Mao Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities during differentiation. This is incorrect for <jats:italic>parametric discontinuities</jats:italic> —conditionals containing at least one real-valued parameter and at least one variable of integration. We introduce Potto, the first differentiable first-order programming language to soundly differentiate parametric discontinuities. We present a denotational semantics for programs and program derivatives and show the two accord. We describe the implementation of Potto, which enables separate compilation of programs. Our prototype implementation overcomes previous compile-time bottlenecks achieving an 88.1x and 441.2x speed up in compile time and a 2.5x and 7.9x speed up in runtime, respectively, on two increasingly large image stylization benchmarks. We showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders. 2024-05-03T15:40:39Z 2024-05-03T15:40:39Z 2024-04-29 2024-05-01T07:48:33Z Article http://purl.org/eprint/type/JournalArticle 2475-1421 https://hdl.handle.net/1721.1/154393 Michel, Jesse, Mu, Kevin, Yang, Xuanda, Bangaru, Sai Praveen, Collins, Elias Rojas et al. 2024. "Distributions for Compositionally Differentiating Parametric Discontinuities." Proceedings of the ACM on Programming Languages, 8 (OOPSLA1). PUBLISHER_CC en 10.1145/3649843 Proceedings of the ACM on Programming Languages Creative Commons Attribution-Noncommercial-ShareAlike https://creativecommons.org/licenses/by-sa/4.0/ The author(s) application/pdf Association for Computing Machinery Association for Computing Machinery |
| spellingShingle | Michel, Jesse Mu, Kevin Yang, Xuanda Bangaru, Sai Praveen Collins, Elias Rojas Bernstein, Gilbert Ragan-Kelley, Jonathan Carbin, Michael Li, Tzu-Mao Distributions for Compositionally Differentiating Parametric Discontinuities |
| title | Distributions for Compositionally Differentiating Parametric Discontinuities |
| title_full | Distributions for Compositionally Differentiating Parametric Discontinuities |
| title_fullStr | Distributions for Compositionally Differentiating Parametric Discontinuities |
| title_full_unstemmed | Distributions for Compositionally Differentiating Parametric Discontinuities |
| title_short | Distributions for Compositionally Differentiating Parametric Discontinuities |
| title_sort | distributions for compositionally differentiating parametric discontinuities |
| url | https://hdl.handle.net/1721.1/154393 |
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