Differentiable Programming for Piecewise Polynomial Functions
Differentiable Programming for Piecewise Polynomial Functions
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分段多项式函数的可微规划
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
C. Hegde
中科院分区：
文献类型：
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作者：
Minsu Cho;Ameya Joshi;Xian Yeow Lee;Aditya Balu;A. Krishnamurthy;B. Ganapathysubramanian;S. Sarkar;C. Hegde
我们介绍了一种新的、原则性的方法，将基于梯度的优化扩展到分段平滑模型，如k-直方图、样条线和分割图。我们导出了这类函数的弱雅可比的精确形式，并表明它呈现出一种块稀疏结构，该结构可以隐式地计算和精确地fi。我们表明，使用重新设计的雅可比矩阵可以提高应用程序的性能，如分段多项式回归模型去噪、无数据生成模型训练和图像分割
We introduce a new, principled approach to extend gradient-based optimization to piecewise smooth models, such as k-histograms, splines, and segmentation maps. We derive an accurate form of the weak Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. We show that using the redesigned Jacobian leads to improved performance in applications such as denoising with piecewise polynomial regression models, data-free generative model training, and image segmentation