2021/10/04 by Cho, Minsu, Balu, Aditya, Joshi, Ameya +6 · 2 citations
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · doi:10.48550/arxiv.2110.01532
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.