# 3DGS2-TR: Scalable Second-Order Trust-Region Method for 3D Gaussian Splatting

arXiv: https://arxiv.org/abs/2602.00395 · HTML: https://mlsanity.com/paper/2602.00395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [A Hierarchical 3D Gaussian Representation for Real-Time Rendering of Very Large Datasets](https://mlsanity.com/paper/2406.12080/) (2024)
- [Mini-Splatting: Representing Scenes with a Constrained Number of Gaussians](https://mlsanity.com/paper/2403.14166/) (2024)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [EAGLES: Efficient Accelerated 3D Gaussians with Lightweight EncodingS](https://mlsanity.com/paper/2312.04564/) (2023)
- [Reducing the Memory Footprint of 3D Gaussian Splatting](https://mlsanity.com/paper/2406.17074/) (2024)
- [CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization](https://mlsanity.com/paper/2405.12110/) (2024)
- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives](https://mlsanity.com/paper/2412.00578/) (2024)
- [FlashGS: Efficient 3D Gaussian Splatting for Large-scale and High-resolution Rendering](https://mlsanity.com/paper/2408.07967/) (2024)
- [DropGaussian: Structural Regularization for Sparse-view Gaussian Splatting](https://mlsanity.com/paper/2504.00773/) (2025)
- [LP-3DGS: Learning to Prune 3D Gaussian Splatting](https://mlsanity.com/paper/2405.18784/) (2024)
- [On Scaling Up 3D Gaussian Splatting Training](https://mlsanity.com/paper/2406.18533/) (2024)
- [Trimming the Fat: Efficient Compression of 3D Gaussian Splats through Pruning](https://mlsanity.com/paper/2406.18214/) (2024)
- [3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt](https://mlsanity.com/paper/2409.12892/) (2024)
- [DISTWAR: Fast Differentiable Rendering on Raster-based Rendering Pipelines](https://mlsanity.com/paper/2401.05345/) (2023)
- [AdR-Gaussian: Accelerating Gaussian Splatting with Adaptive Radius](https://mlsanity.com/paper/2409.08669/) (2024)
- [3DGS2: Near Second-order Converging 3D Gaussian Splatting](https://mlsanity.com/paper/2501.13975/) (2025)
- [City-on-Web: Real-time Neural Rendering of Large-scale Scenes on the Web](https://mlsanity.com/paper/2312.16457/) (2023)

## Abstract (arXiv)

We propose 3DGS2-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 (H"ollein 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, 3DGS2-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.