[论文] TorchCurves: Differentiable Parametric Curves

论文概要

研究领域: ML
作者: Alex Shtoff
发布时间: 2026-11-10
arXiv: 2611.14516

中文摘要

我们提出 TorchCurves：一个将向量值参数化曲线视为可学习基本单元的 PyTorch 库。其核心操作将批量标量输入映射到以 B 样条或勒让德多项式基表示的曲线上，支持对输入与系数的双向微分。曲线系数可与外围模型联合优化，也可由另一网络生成。该库提供可训练模块、可复用基模块与函数式接口，支持从连续特征嵌入到 Kolmogorov-Arnold 网络（KAN）再到函数回归等多种应用。实现上将经典求值算法与向量化 PyTorch 操作结合，强调可读性与可维护性，无需自定义硬件内核。计时实验将曲线求值与 NumPy/SciPy 对比、KAN 训练与 EfficientKAN 对比，展示了这一通用性在哪些场景下计算可行、哪些场景开销显著。代码：github.com/alexshtf/torchcurves。

原文摘要

We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing exper...

自动采集于 2026-11-12

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