# Splat Feature Solver

arXiv: https://arxiv.org/abs/2508.12216 · HTML: https://mlsanity.com/paper/2508.12216/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 44 references that are in the map.
- First posted on arXiv 17 Aug 2025.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Language-driven Semantic Segmentation](https://mlsanity.com/paper/2201.03546/) (2022)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [LERF: Language Embedded Radiance Fields](https://mlsanity.com/paper/2303.09553/) (2023)
- [LangSplat: 3D Language Gaussian Splatting](https://mlsanity.com/paper/2312.16084/) (2023)
- [Gaussian Grouping: Segment and Edit Anything in 3D Scenes](https://mlsanity.com/paper/2312.00732/) (2023)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [Language Embedded 3D Gaussians for Open-Vocabulary Scene Understanding](https://mlsanity.com/paper/2311.18482/) (2023)
- [MaskCLIP: Masked Self-Distillation Advances Contrastive Language-Image Pretraining](https://mlsanity.com/paper/2208.12262/) (2022)
- [Segment Any 3D Gaussians](https://mlsanity.com/paper/2312.00860/) (2023)
- [OpenGaussian: Towards Point-Level 3D Gaussian-based Open Vocabulary Understanding](https://mlsanity.com/paper/2406.02058/) (2024)
- [Weakly Supervised 3D Open-vocabulary Segmentation](https://mlsanity.com/paper/2305.14093/) (2023)
- [FeatUp: A Model-Agnostic Framework for Features at Any Resolution](https://mlsanity.com/paper/2403.10516/) (2024)
- [FMGS: Foundation Model Embedded 3D Gaussian Splatting for Holistic 3D Scene Understanding](https://mlsanity.com/paper/2401.01970/) (2024)
- [Semantic Gaussians: Open-Vocabulary Scene Understanding with 3D Gaussian Splatting](https://mlsanity.com/paper/2403.15624/) (2024)
- [StyleGaussian: Instant 3D Style Transfer with Gaussian Splatting](https://mlsanity.com/paper/2403.07807/) (2024)
- [Dr. Splat: Directly Referring 3D Gaussian Splatting via Direct Language Embedding Registration](https://mlsanity.com/paper/2502.16652/) (2025)
- [EgoLifter: Open-world 3D Segmentation for Egocentric Perception](https://mlsanity.com/paper/2403.18118/) (2024)
- [Feature Splatting: Language-Driven Physics-Based Scene Synthesis and Editing](https://mlsanity.com/paper/2404.01223/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [N2F2: Hierarchical Scene Understanding with Nested Neural Feature Fields](https://mlsanity.com/paper/2403.10997/) (2024)

## Built on by (most cited first, 7 of 7)

- [ReLaGS: Relational Language Gaussian Splatting](https://mlsanity.com/paper/2603.17605/) (2026)
- [Consistent Instance Field for Dynamic Scene Understanding](https://mlsanity.com/paper/2512.14126/) (2025)
- [Universal Beta Splatting](https://mlsanity.com/paper/2510.03312/) (2025)
- [NanoGS: Training-Free Gaussian Splat Simplification](https://mlsanity.com/paper/2603.16103/) (2026)
- [LangStreet: Persistent Language Fields for Anchor-Decoded Street Gaussians](https://mlsanity.com/paper/2609.11616/) (2026)
- [NormLift: From Lifted Features To Semantic Reliability In 3D Gaussian Splatting](https://mlsanity.com/paper/2609.18898/) (2026)
- [DIGS: Distribution-Informed Gaussian Splatting for Training-Free Open-Vocabulary 3D Segmentation](https://mlsanity.com/paper/2610.16177/) (2026)

## Abstract (arXiv)

Feature lifting has emerged as a crucial component in 3D scene understanding, enabling the attachment of rich image feature descriptors (e.g., DINO, CLIP) onto splat-based 3D representations. The core challenge lies in optimally assigning rich general attributes to 3D primitives while addressing the inconsistency issues from multi-view images. We present a unified, kernel- and feature-agnostic formulation of the feature lifting problem as a sparse linear inverse problem, which can be solved efficiently in closed form. Our approach admits a provable upper bound on the global optimal error under convex losses for delivering high quality lifted features. To address inconsistencies and noise in multi-view observations, we introduce two complementary regularization strategies to stabilize the solution and enhance semantic fidelity. Tikhonov Guidance enforces numerical stability through soft diagonal dominance, while Post-Lifting Aggregation filters noisy inputs via feature clustering. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on open-vocabulary 3D segmentation benchmarks, outperforming training-based, grouping-based, and heuristic-forward baselines while producing lifted features in minutes. Our code is available in the hrefhttps://github.com/saliteta/splat-distiller/tree/maintextcolorblueGitHub. We provide additional hrefhttps://splat-distiller.pages.dev/textcolorbluewebsite for more visualization, as well as the hrefhttps://www.youtube.com/watch?v=CH-G5hbvArMtextcolorbluevideo.