Differentiable Spline Approximations

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2021-10-04
Authors
Cho, Minsu
Balu, Aditya
Joshi, Ameya
Prasad, Anjana Deva
Khara, Biswajit
Sarkar, Soumik
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arXiv
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Krishnamurthy, Adarsh
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Mechanical Engineering
The Department of Mechanical Engineering at Iowa State University is where innovation thrives and the impossible is made possible. This is where your passion for problem-solving and hands-on learning can make a real difference in our world. Whether you’re helping improve the environment, creating safer automobiles, or advancing medical technologies, and athletic performance, the Department of Mechanical Engineering gives you the tools and talent to blaze your own trail to an amazing career.
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Electrical and Computer Engineering

The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.

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The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.

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1909-present

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  • Department of Electrical Engineering (1909-1985)
  • Department of Electrical Engineering and Computer Engineering (1985-1995)

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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.
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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.
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