# Learnable Infinite Taylor Gaussian for Dynamic View Rendering

arXiv: https://arxiv.org/abs/2412.04282 · HTML: https://mlsanity.com/paper/2412.04282/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Builds on (most cited first, 30 of 31)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [FSGS: Real-Time Few-shot View Synthesis using Gaussian Splatting](https://mlsanity.com/paper/2312.00451/) (2023)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [3DGStream: On-the-Fly Training of 3D Gaussians for Efficient Streaming of Photo-Realistic Free-Viewpoint Videos](https://mlsanity.com/paper/2403.01444/) (2024)
- [Mixed Neural Voxels for Fast Multi-view Video Synthesis](https://mlsanity.com/paper/2212.00190/) (2022)
- [Streaming Radiance Fields for 3D Video Synthesis](https://mlsanity.com/paper/2210.14831/) (2022)
- [3D Geometry-aware Deformable Gaussian Splatting for Dynamic View Synthesis](https://mlsanity.com/paper/2404.06270/) (2024)
- [HiFi4G: High-Fidelity Human Performance Rendering via Compact Gaussian Splatting](https://mlsanity.com/paper/2312.03461/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Temporal Interpolation Is All You Need for Dynamic Neural Radiance Fields](https://mlsanity.com/paper/2302.09311/) (2023)
- [GeoGaussian: Geometry-aware Gaussian Splatting for Scene Rendering](https://mlsanity.com/paper/2403.11324/) (2024)
- [SWinGS: Sliding Windows for Dynamic 3D Gaussian Splatting](https://mlsanity.com/paper/2312.13308/) (2023)
- [GaussianCube: A Structured and Explicit Radiance Representation for 3D Generative Modeling](https://mlsanity.com/paper/2403.19655/) (2024)
- [SurfelWarp: Efficient Non-Volumetric Single View Dynamic Reconstruction](https://mlsanity.com/paper/1904.13073/) (2019)
- [Sparse Data Driven Mesh Deformation](https://mlsanity.com/paper/1709.01250/) (2017)
- [Unsupervised Low-light Image Enhancement with Lookup Tables and Diffusion Priors](https://mlsanity.com/paper/2409.18899/) (2024)
- [SmileSplat: Generalizable Gaussian Splats for Unconstrained Sparse Images](https://mlsanity.com/paper/2411.18072/) (2024)

## Built on by (most cited first, 11 of 11)

- [4D Gaussian Splatting SLAM](https://mlsanity.com/paper/2503.16710/) (2025)
- [Splatography: Sparse multi-view dynamic Gaussian Splatting for filmmaking challenges](https://mlsanity.com/paper/2511.05152/) (2025)
- [ProDyG: Progressive Dynamic Scene Reconstruction via Gaussian Splatting from Monocular Videos](https://mlsanity.com/paper/2509.17864/) (2025)
- [RU4D-SLAM: Reweighting Uncertainty in Gaussian Splatting SLAM for 4D Scene Reconstruction](https://mlsanity.com/paper/2602.20807/) (2026)
- [Reconstructing the Dynamic World: A Representation-Centric View of 4D Scene Reconstruction](https://mlsanity.com/paper/2609.39960/) (2026)
- [CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions](https://mlsanity.com/paper/2602.01844/) (2026)
- [Relaxed Rigidity with Ray-based Grouping for Dynamic Gaussian Splatting](https://mlsanity.com/paper/2603.24994/) (2026)
- [ReFlow: Self-correction Motion Learning for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2604.01561/) (2026)
- [DSD-GS: Dynamic-Static Decomposition of Gaussian Splatting for Efficient and High-Fidelity Dynamic Scene Reconstruction](https://mlsanity.com/paper/2605.30863/) (2026)
- [DyG2T: Modeling Object Dynamics with 3D Gaussian Temporal-Spatial Particle Graph Transformer](https://mlsanity.com/paper/2608.18498/) (2026)
- [TruncGradGS: Improved 3D Gaussian Splatting via Truncated Gradient Updates](https://mlsanity.com/paper/2609.03534/) (2026)

## Abstract (arXiv)

Capturing the temporal evolution of Gaussian properties such as position, rotation, and scale is a challenging task due to the vast number of time-varying parameters and the limited photometric data available, which generally results in convergence issues, making it difficult to find an optimal solution. While feeding all inputs into an end-to-end neural network can effectively model complex temporal dynamics, this approach lacks explicit supervision and struggles to generate high-quality transformation fields. On the other hand, using time-conditioned polynomial functions to model Gaussian trajectories and orientations provides a more explicit and interpretable solution, but requires significant handcrafted effort and lacks generalizability across diverse scenes. To overcome these limitations, this paper introduces a novel approach based on a learnable infinite Taylor Formula to model the temporal evolution of Gaussians. This method offers both the flexibility of an implicit network-based approach and the interpretability of explicit polynomial functions, allowing for more robust and generalizable modeling of Gaussian dynamics across various dynamic scenes. Extensive experiments on dynamic novel view rendering tasks are conducted on public datasets, demonstrating that the proposed method achieves state-of-the-art performance in this domain. More information is available on our project page(https://ellisonking.github.io/TaylorGaussian).