# 3DGS2: Near Second-order Converging 3D Gaussian Splatting

arXiv: https://arxiv.org/abs/2501.13975 · HTML: https://mlsanity.com/paper/2501.13975/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [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)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [Mixture of Volumetric Primitives for Efficient Neural Rendering](https://mlsanity.com/paper/2103.01954/) (2021)
- [Deferred Neural Rendering: Image Synthesis using Neural Textures](https://mlsanity.com/paper/1904.12356/) (2019)
- [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)
- [Stereo Magnification: Learning View Synthesis using Multiplane Images](https://mlsanity.com/paper/1805.09817/) (2018)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [EAGLES: Efficient Accelerated 3D Gaussians with Lightweight EncodingS](https://mlsanity.com/paper/2312.04564/) (2023)
- [Point-Based Neural Rendering with Per-View Optimization](https://mlsanity.com/paper/2109.02369/) (2021)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [BundleFusion: Real-time Globally Consistent 3D Reconstruction using On-the-fly Surface Re-integration](https://mlsanity.com/paper/1604.01093/) (2016)
- [Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives](https://mlsanity.com/paper/2412.00578/) (2024)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [FlashGS: Efficient 3D Gaussian Splatting for Large-scale and High-resolution Rendering](https://mlsanity.com/paper/2408.07967/) (2024)
- [Differentiable Point-Based Radiance Fields for Efficient View Synthesis](https://mlsanity.com/paper/2205.14330/) (2022)
- [3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt](https://mlsanity.com/paper/2409.12892/) (2024)
- [AdR-Gaussian: Accelerating Gaussian Splatting with Adaptive Radius](https://mlsanity.com/paper/2409.08669/) (2024)

## Built on by (most cited first, 19 of 19)

- [FastGS: Training 3D Gaussian Splatting in 100 Seconds](https://mlsanity.com/paper/2511.04283/) (2025)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [Anti-Aliased 2D Gaussian Splatting](https://mlsanity.com/paper/2506.11252/) (2025)
- [Matrix-free Second-order Optimization of Gaussian Splats with Residual Sampling](https://mlsanity.com/paper/2504.12905/) (2025)
- [Speeding Up the Learning of 3D Gaussians with Much Shorter Gaussian Lists](https://mlsanity.com/paper/2603.09277/) (2026)
- [Generative 3D Gaussians with Learned Density Control](https://mlsanity.com/paper/2605.16355/) (2026)
- [TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting](https://mlsanity.com/paper/2506.13348/) (2025)
- [OnlineSplatter: Pose-Free Online 3D Reconstruction for Free-Moving Objects](https://mlsanity.com/paper/2510.20605/) (2025)
- [PocketGS: On-Device Training of 3D Gaussian Splatting for High Perceptual Modeling](https://mlsanity.com/paper/2601.17354/) (2026)
- [Variation-aware Flexible 3D Gaussian Editing](https://mlsanity.com/paper/2602.11638/) (2026)
- [TideGS: Scalable Training of Over One Billion 3D Gaussian Splatting Primitives via Out-of-Core Optimization](https://mlsanity.com/paper/2605.20150/) (2026)
- [Learn2Splat: Extending the Horizon of Learned 3DGS Optimization](https://mlsanity.com/paper/2605.15760/) (2026)
- [TRSVR: An Adaptive Stochastic Trust-Region Method with Variance Reduction](https://mlsanity.com/paper/2601.14647/) (2026)
- [3DGS2-TR: Scalable Second-Order Trust-Region Method for 3D Gaussian Splatting](https://mlsanity.com/paper/2602.00395/) (2026)
- [FTSplat: Feed-forward Triangle Splatting Network](https://mlsanity.com/paper/2603.05932/) (2026)
- [Faster 3D Gaussian Splatting Convergence via Structure-Aware Densification](https://mlsanity.com/paper/2604.28016/) (2026)
- [SparseOIT: Improving Order-Independent Transparency 3DGS via Active Set Method](https://mlsanity.com/paper/2605.13855/) (2026)
- [Exploration Matters for Escaping the Blur Trap in 3D Gaussian Splatting](https://mlsanity.com/paper/2607.17965/) (2026)
- [Laplacian Frequency Hierarchies for Efficient 3D Gaussian Splatting Training](https://mlsanity.com/paper/2609.03334/) (2026)

## Abstract (arXiv)

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.