Differentiable Spline Approximations
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.
Code (0)
등록된 구현이 없습니다.
Tasks
3D Point Cloud ReconstructionBIG-bench Machine LearningFormImage SegmentationPoint cloud reconstructionSemantic SegmentationSimilar Papers 제목 키워드 기반
Spline refinement with differentiable rendering
Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We…
Drug DiscoveryNeural Diffeomorphic Non-uniform B-spline Flows
Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibili…
NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics
Differentiable rendering of planar rational splines remains largely underexplored, despite their widespread use in vector graphics and design. Existing differentiable vector renderers primarily focus on Bézier curves and…
Quantum Splines for Non-Linear Approximations
Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that ham…
Binary segmentation of medical images using implicit spline representations and deep learning
We propose a novel approach to image segmentation based on combining implicit spline representations with deep convolutional neural networks. This is done by predicting the control points of a bivariate spline function w…
Image SegmentationSegmentationSemantic Segmentation