用高斯-牛顿法加速形状学习，收敛更快更稳。
Gauss-Newton Natural Gradient Descent for Shape Learning
- 引入高斯-牛顿优化解决形状学习中的病态约束问题。
- 相比一阶方法，迭代次数大幅减少，训练速度与精度同步提升。
- 适合需要高效精确建模的几何深度学习任务。
我们研究了在形状学习（包括隐式神经表面和几何感知神经网络）中使用高斯-牛顿法进行优化。该方法解决了形状学习中的关键挑战，如底层微分约束的病态性，以及参数空间优化问题与函数空间自然表述之间的不匹配。实验表明，该方法在基准形状优化任务中显著提升了收敛速度和稳定性，同时所需迭代次数远少于标准一阶方法，并一致改善了训练速度和最终解的准确性。
原文摘要 · Abstract (English)
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning of the underlying differential constraints and the mismatch between the optimization problem in parameter space and the function space where the problem is naturally posed. This leads to significantly faster and more stable convergence than standard first-order methods, while also requiring far fewer iterations. Experiments across benchmark shape optimization tasks demonstrate that the Gauss-Newton method consistently improves both training speed and final solution accuracy.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。