# Softmax-GS: Generalized Gaussians Learning When to Blend or Bound

arXiv: https://arxiv.org/abs/2604.27437 · HTML: https://mlsanity.com/paper/2604.27437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (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)
- [Octree-GS: Towards Consistent Real-time Rendering with LOD-Structured 3D Gaussians](https://mlsanity.com/paper/2403.17898/) (2024)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [VastGaussian: Vast 3D Gaussians for Large Scene Reconstruction](https://mlsanity.com/paper/2402.17427/) (2024)
- [CityGaussian: Real-time High-quality Large-Scale Scene Rendering with Gaussians](https://mlsanity.com/paper/2404.01133/) (2024)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (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)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [AbsGS: Recovering Fine Details for 3D Gaussian Splatting](https://mlsanity.com/paper/2404.10484/) (2024)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [3D-HGS: 3D Half-Gaussian Splatting](https://mlsanity.com/paper/2406.02720/) (2024)
- [Efficient Perspective-Correct 3D Gaussian Splatting Using Hybrid Transparency](https://mlsanity.com/paper/2410.08129/) (2024)
- [Sort-free Gaussian Splatting via Weighted Sum Rendering](https://mlsanity.com/paper/2410.18931/) (2024)
- [SAGS: Structure-Aware 3D Gaussian Splatting](https://mlsanity.com/paper/2404.19149/) (2024)
- [StochasticSplats: Stochastic Rasterization for Sorting-Free 3D Gaussian Splatting](https://mlsanity.com/paper/2503.24366/) (2025)
- [Deformable Radial Kernel Splatting](https://mlsanity.com/paper/2412.11752/) (2024)
- [3D Student Splatting and Scooping](https://mlsanity.com/paper/2503.10148/) (2025)
- [DisC-GS: Discontinuity-aware Gaussian Splatting](https://mlsanity.com/paper/2405.15196/) (2024)
- [Lightweight Predictive 3D Gaussian Splats](https://mlsanity.com/paper/2406.19434/) (2024)

## Abstract (arXiv)

3D Gaussian Splatting (3D GS) is widely adopted for novel view synthesis due to its high training and rendering efficiency. However, its efficiency relies on the key assumption that Gaussians do not overlap in the 3D space, which leads to noticeable artifacts and view inconsistencies. In addition, the inherently diffuse boundaries of Gaussians hinder accurate reconstruction of sharp object edges. We propose Softmax-GS, a unified solution that addresses both the view-inconsistency and the diffuse-boundary problem by enforcing a softmax-based competition in overlapping regions between two Gaussians. With learnable parameters controlling the strength of the competition, it enables a continuous spectrum from smooth color blending to crisp, well-defined boundaries. Our formulation explicitly preserves order invariance for any two overlapping Gaussians and ensures that the output transmittance remains unchanged irrespective of the extent of overlapping, preventing undesirable discontinuities in the rendered output. Ablation experiments on simple geometries demonstrate the effectiveness of each component of Softmax-GS, and evaluations on real-world benchmarks show that it achieves state-of-the-art performance, improving both reconstruction quality and parameter efficiency.