3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior efficiency. As a learning-based approach, 3DGS training has been dealt with the standard stochastic gradient descent (SGD) method, which offers at most linear convergence. Consequently, training often requires tens of minutes, even with GPU acceleration. This paper introduces a (near) second-order convergent training algorithm for 3DGS, leveraging its unique properties. Our approach is inspired by two key observations. First, the attributes of a Gaussian kernel contribute independently to the image-space loss, which endorses isolated and local optimization algorithms. We exploit this by splitting the optimization at the level of individual kernel attributes, analytically constructing small-size Newton systems for each parameter group, and efficiently solving these systems on GPU threads. This achieves Newton-like convergence per training image without relying on the global Hessian. Second, kernels exhibit sparse and structured coupling across input images. This property allows us to effectively utilize spatial information to mitigate overshoot during stochastic training. Our method converges an order faster than standard GPU-based 3DGS training, requiring over 10× fewer iterations while maintaining or surpassing the quality of the compared with the SGD-based 3DGS reconstructions.
3D高斯点云（3DGS）已成为新视角合成和3D重建的主流解决方案。通过显式地使用一组高斯核编码3D场景，3DGS实现了高质量的渲染并具有卓越的效率。作为一种基于学习的方法，3DGS的训练通常使用标准的随机梯度下降（SGD）方法，这种方法最多只能实现线性收敛。因此，即使在GPU加速的情况下，训练过程通常也需要数十分钟。本文提出了一种（接近）二阶收敛的训练算法，针对3DGS的独特性质进行优化。我们的方法受到两个关键观察的启发。首先，高斯核的属性对图像空间损失的贡献是独立的，这支持局部优化算法。我们通过在单个核属性级别拆分优化，分析性地构建每个参数组的小型牛顿系统，并在GPU线程上高效求解这些系统，从而实现每个训练图像的类似牛顿收敛，而不依赖于全局Hessian矩阵。其次，高斯核在输入图像之间表现出稀疏且结构化的耦合特性。这一特性使我们能够有效利用空间信息，以减轻在随机训练过程中的过冲问题。与标准的GPU基础3DGS训练方法相比，我们的方法收敛速度快了一倍以上，迭代次数减少了超过10倍，同时在质量上与基于SGD的3DGS重建相当或更优。