# ResFields: Residual Neural Fields for Spatiotemporal Signals

arXiv: https://arxiv.org/abs/2309.03160 · HTML: https://mlsanity.com/paper/2309.03160/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 74 references that are in the map.
- First posted on arXiv 6 Sep 2023.

## Builds on (most cited first, 30 of 56)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)

## Built on by (most cited first, 27 of 27)

- [Align Your Gaussians: Text-to-4D with Dynamic 3D Gaussians and Composed Diffusion Models](https://mlsanity.com/paper/2312.13763/) (2023)
- [SplatFields: Neural Gaussian Splats for Sparse 3D and 4D Reconstruction](https://mlsanity.com/paper/2409.11211/) (2024)
- [VideoRF: Rendering Dynamic Radiance Fields as 2D Feature Video Streams](https://mlsanity.com/paper/2312.01407/) (2023)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [Hybrid 3D-4D Gaussian Splatting for Fast Dynamic Scene Representation](https://mlsanity.com/paper/2505.13215/) (2025)
- [SwinGS: Sliding Window Gaussian Splatting for Volumetric Video Streaming with Arbitrary Length](https://mlsanity.com/paper/2409.07759/) (2024)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [Creating a Digital Twin of Spinal Surgery: A Proof of Concept](https://mlsanity.com/paper/2403.16736/) (2024)
- [Physics-Informed Learning of Characteristic Trajectories for Smoke Reconstruction](https://mlsanity.com/paper/2407.09679/) (2024)
- [VolumetricSMPL: A Neural Volumetric Body Model for Efficient Interactions, Contacts, and Collisions](https://mlsanity.com/paper/2506.23236/) (2025)
- [Degrees of Freedom Matter: Inferring Dynamics from Point Trajectories](https://mlsanity.com/paper/2406.03625/) (2024)
- [SpeeDe3DGS: Speedy Deformable 3D Gaussian Splatting with Temporal Pruning and Motion Grouping](https://mlsanity.com/paper/2506.07917/) (2025)
- [TK-Planes: Tiered K-Planes with High Dimensional Feature Vectors for Dynamic UAV-based Scenes](https://mlsanity.com/paper/2405.02762/) (2024)
- [Spline Deformation Field](https://mlsanity.com/paper/2507.07521/) (2025)
- [MorpheuS: Neural Dynamic 360deg Surface Reconstruction from Monocular RGB-D Video](https://mlsanity.com/paper/2312.00778/) (2023)
- [TFS-NeRF: Template-Free NeRF for Semantic 3D Reconstruction of Dynamic Scene](https://mlsanity.com/paper/2409.17459/) (2024)
- [Bias for Action: Video Implicit Neural Representations with Bias Modulation](https://mlsanity.com/paper/2501.09277/) (2025)
- [Neural rendering enables dynamic tomography](https://mlsanity.com/paper/2410.20558/) (2024)
- [Neural Texture Splatting: Expressive 3D Gaussian Splatting for View Synthesis, Geometry, and Dynamic Reconstruction](https://mlsanity.com/paper/2511.18873/) (2025)
- [The Surprising Effectiveness of Noise Pretraining for Implicit Neural Representations](https://mlsanity.com/paper/2603.29034/) (2026)
- [Synergistic Integration of Coordinate Network and Tensorial Feature for Improving Neural Radiance Fields from Sparse Inputs](https://mlsanity.com/paper/2405.07857/) (2024)
- [SyncTrack4D: Cross-Video Motion Alignment and Video Synchronization for Multi-Video 4D Gaussian Splatting](https://mlsanity.com/paper/2512.04315/) (2025)
- [COSMOS: Coherent Supergaussian Modeling with Spatial Priors for Sparse-View 3D Splatting](https://mlsanity.com/paper/2602.06044/) (2025)
- [TG-Field: Geometry-Aware Radiative Gaussian Fields for Tomographic Reconstruction](https://mlsanity.com/paper/2602.11705/) (2026)
- [Spectral Energy Centroid: a Metric for Improving Performance and Analyzing Spectral Bias in Implicit Neural Representations](https://mlsanity.com/paper/2605.12709/) (2026)
- [DLGStream: Dynamic Language-embedded Guassian Splatting for Open-vocabulary Enabled Free-viewpoint Video Streaming](https://mlsanity.com/paper/2606.28840/) (2026)
- [UniFusion: Sparse-View 4D Reconstruction via Unified Spatio-temporal Depth Alignment](https://mlsanity.com/paper/2609.05888/) (2026)

## Abstract (arXiv)

Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, such as signed distance (SDFs) or radiance fields (NeRFs), via a single multi-layer perceptron (MLP). However, despite the power and simplicity of representing signals with an MLP, these methods still face challenges when modeling large and complex temporal signals due to the limited capacity of MLPs. In this paper, we propose an effective approach to address this limitation by incorporating temporal residual layers into neural fields, dubbed ResFields. It is a novel class of networks specifically designed to effectively represent complex temporal signals. We conduct a comprehensive analysis of the properties of ResFields and propose a matrix factorization technique to reduce the number of trainable parameters and enhance generalization capabilities. Importantly, our formulation seamlessly integrates with existing MLP-based neural fields and consistently improves results across various challenging tasks: 2D video approximation, dynamic shape modeling via temporal SDFs, and dynamic NeRF reconstruction. Lastly, we demonstrate the practical utility of ResFields by showcasing its effectiveness in capturing dynamic 3D scenes from sparse RGBD cameras of a lightweight capture system.