text: 173,227,1445469040944848896,135114281,Ameya Joshi,Our NeurIPS-2021 paper on Differentiable Spline Approximations is now on @arxiv_org : <LINK>. We propose gradient based optimization for splines and show some really cool applications in 3D reconstruction and PDEs! @chomd90 @BabuaSpeaks @baskinscience @adarshk,https://arxiv.org/abs/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. ",Differentiable Spline Approximations,1,['Our NeurIPS-2021 paper on Differentiable Spline Approximations is now on @arxiv_org : <LINK>. We propose gradient based optimization for splines and show some really cool applications in 3D reconstruction and PDEs!\n@chomd90 @BabuaSpeaks @baskinscience @adarshk'],21,10,260