用更少迭代和更低内存，加速3D高斯点阵的训练过程。
3DGS$^2$-TR: Scalable Second-Order Trust-Region Method for 3D Gaussian Splatting
- 仅用海森矩阵对角线近似曲率，实现无矩阵计算。
- 相比ADAM减少50%训练步数，峰值显存增加不足1GB。
- 适合大规模场景训练，支持分布式扩展。
我们提出3DGS$^2$-TR，一种用于加速3D高斯点阵（3DGS）场景训练的二阶优化方法。不同于依赖显式或稠密曲率表示的现有方法（如3DGS-LM或3DGS2），本方法通过Hutchinson法仅以海森矩阵对角线近似曲率，实现完全无矩阵计算，计算与内存复杂度均与ADAM相当，为O(n)。为应对3DGS光栅化过程中的强非线性，引入基于平方赫林格距离的参数级信任域机制，对高斯参数更新进行正则化。在相同初始化且不进行密度增长的情况下，3DGS$^2$-TR在标准数据集上达到更优重建质量，训练迭代次数减少50%，峰值GPU显存开销低于1GB（比ADAM多17%，比3DGS-LM低85%），具备扩展至超大场景及分布式训练的潜力。
原文摘要 · Abstract (English)
We propose 3DGS$^2$-TR,a second-order optimizer for accelerating the scene training problem in 3D Gaussian Splatting (3DGS). Unlike existing second-order approaches that rely on explicit or dense curvature representations, such as 3DGS-LM (Höllein et al., 2025) or 3DGS2 (Lan et al., 2025), our method approximates curvature using only the diagonal of the Hessian matrix, efficiently via Hutchinson's method. Our approach is fully matrix-free and has the same complexity as ADAM (Kingma, 2024), $O(n)$ in both computation and memory costs. To ensure stable optimization in the presence of strong nonlinearity in the 3DGS rasterization process, we introduce a parameter-wise trust-region technique based on the squared Hellinger distance, regularizing updates to Gaussian parameters. Under identical parameter initialization and without densification, 3DGS$^2$-TR is able to achieve better reconstruction quality on standard datasets, using 50% fewer training iterations compared to ADAM, while incurring less than 1GB of peak GPU memory overhead (17% more than ADAM and 85% less than 3DGS-LM), enabling scalability to very large scenes and potentially to distributed training settings.
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