Differentiable Spline Approximations

dc.contributor.author Cho, Minsu
dc.contributor.author Balu, Aditya
dc.contributor.author Joshi, Ameya
dc.contributor.author Prasad, Anjana Deva
dc.contributor.author Khara, Biswajit
dc.contributor.author Sarkar, Soumik
dc.contributor.author Ganapathysubramanian, Baskar
dc.contributor.author Krishnamurthy, Adarsh
dc.contributor.department Mechanical Engineering
dc.contributor.department Electrical and Computer Engineering
dc.date.accessioned 2024-02-14T17:48:57Z
dc.date.available 2024-02-14T17:48:57Z
dc.date.issued 2021-10-04
dc.description.abstract The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable "layer" in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis.
dc.description.comments This is a proceeding preprint from Cho, Minsu, Aditya Balu, Ameya Joshi, Anjana Deva Prasad, Biswajit Khara, Soumik Sarkar, Baskar Ganapathysubramanian, Adarsh Krishnamurthy, and Chinmay Hegde. "DIFFERENTIABLE SPLINE APPROXIMATIONS." arXiv preprint arXiv:2110.01532 (2021). doi: https://doi.org/10.48550/arXiv.2110.01532. Copyright 2021 The Authors.
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/JvNVD1mv
dc.language.iso en
dc.publisher arXiv
dc.source.uri https://doi.org/10.48550/arXiv.2110.01532 *
dc.subject.disciplines DegreeDisciplines::Engineering::Mechanical Engineering::Electro-Mechanical Systems
dc.subject.disciplines DegreeDisciplines::Engineering::Electrical and Computer Engineering::Electronic Devices and Semiconductor Manufacturing
dc.subject.keywords Differentiable NURBS Layer
dc.subject.keywords NURBS
dc.subject.keywords Geometric Deep Learning
dc.subject.keywords Surface Modeling
dc.title Differentiable Spline Approximations
dc.type Preprint
dspace.entity.type Publication
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