Automatic Local Inverse Calculation for Change of Variables
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3689491.3689970.pdf
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557.56 KB
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Adobe PDF
Checksum (MD5)
531f9176a92bf62f58b8d2521c2f9947
Author(s)
Rojas Collins, Elias
Date Issued
October 20, 2024
Publisher
ACM|Companion Proceedings of the 2024 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity
Citation
Rojas Collins, Elias. 2024. "Automatic Local Inverse Calculation for Change of Variables."
Version
Final published version
Abstract
Inversion is a fundamental operation that arises frequently in probabilistic inference and computer graphics. For example, inversion is used to decrease variance and to enable differentiation in variational inference (e.g., reparameterization trick) and in differentiable rendering (e.g., to integrate over object boundaries). Existing approaches to inversion limit the class of functions inverted, for example, to affine functions, or require a user-specified inverse. We study when a local inverse—an inverse that is valid in a neighborhood of a point—exists. We provide an algorithm to approximate the local inverse and give the convergence rate of the solver. We present LIN, a system that automatically computes the local inverse of a function using a fixed-point solver. We implement LIN in Python and use it to automatically compute the local inverse of affine, polar, and hyperbolic changes of variables arising in image stylization.
Description
SPLASH Companion ’24, October 20–25, 2024, Pasadena, CA, USA
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3689491.3689970
