# Expansive Supervision for Neural Radiance Field

arXiv: https://arxiv.org/abs/2409.08056 · HTML: https://mlsanity.com/paper/2409.08056/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Make-It-3D: High-Fidelity 3D Creation from A Single Image with Diffusion Prior](https://mlsanity.com/paper/2303.14184/) (2023)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [Panoptic Lifting for 3D Scene Understanding with Neural Fields](https://mlsanity.com/paper/2212.09802/) (2022)
- [DeRF: Decomposed Radiance Fields](https://mlsanity.com/paper/2011.12490/) (2020)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [NeRF-Art: Text-Driven Neural Radiance Fields Stylization](https://mlsanity.com/paper/2212.08070/) (2022)
- [Real-Time Neural Light Field on Mobile Devices](https://mlsanity.com/paper/2212.08057/) (2022)
- [Strivec: Sparse Tri-Vector Radiance Fields](https://mlsanity.com/paper/2307.13226/) (2023)
- [Convergence Analysis of Distributed Stochastic Gradient Descent with Shuffling](https://mlsanity.com/paper/1709.10432/) (2017)
- [Mirror-NeRF: Learning Neural Radiance Fields for Mirrors with Whitted-Style Ray Tracing](https://mlsanity.com/paper/2308.03280/) (2023)

## Built on by (most cited first, 5 of 5)

- [Optimizing Rank for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2512.14366/) (2025)
- [SizeGS: Size-aware Compression of 3D Gaussian Splatting via Mixed Integer Programming](https://mlsanity.com/paper/2412.05808/) (2024)
- [EVOS: Efficient Implicit Neural Training via EVOlutionary Selector](https://mlsanity.com/paper/2412.10153/) (2024)
- [SD-GS: Structured Deformable 3D Gaussians for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2507.07465/) (2025)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)

## Abstract (arXiv)

Neural Radiance Field (NeRF) has achieved remarkable success in creating immersive media representations through its exceptional reconstruction capabilities. However, the computational demands of dense forward passes and volume rendering during training continue to challenge its real-world applications. In this paper, we introduce Expansive Supervision to reduce time and memory costs during NeRF training from the perspective of partial ray selection for supervision. Specifically, we observe that training errors exhibit a long-tail distribution correlated with image content. Based on this observation, our method selectively renders a small but crucial subset of pixels and expands their values to estimate errors across the entire area for each iteration. Compared to conventional supervision, our approach effectively bypasses redundant rendering processes, resulting in substantial reductions in both time and memory consumption. Experimental results demonstrate that integrating Expansive Supervision within existing state-of-the-art acceleration frameworks achieves 52% memory savings and 16% time savings while maintaining comparable visual quality.