---
title: "Instant Neural Graphics Primitives with a Multiresolution Hash"
description: "Müller et al. propose a multiresolution hash encoding to fix this. 55 references, cited by 239 papers here."
authors: ["Thomas Muller", "Alex Evans", "Christoph Schied", "Alexander Keller"]
year: 2022
venue: "arXiv:2201.05989 · ACM Trans. Graph. 41, 4, Article 102 (July 2022), 15 pages"
source: "https://arxiv.org/abs/2201.05989"
doi: "10.1145/3528223.3530127"
arxiv: "2201.05989"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/muller-2022-instant-neural-graphics-primitives-multiresolution/"
---
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# Instant Neural Graphics Primitives with a Multiresolution Hash Encoding

**Authors:** [Thomas Muller](https://md.research.elamur.ai/free/en/authors/thomas-muller/), Alex Evans, Christoph Schied and Alexander Keller · **Year:** 2022 · **Venue:** arXiv:2201.05989 · ACM Trans. Graph. 41, 4, Article 102 (July 2022), 15 pages · **Publisher:** [Association for Computing Machinery](https://md.research.elamur.ai/free/en/publishers/association-for-computing-machinery/) · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://doi.org/10.1145/3528223.3530127) · [PDF](https://arxiv.org/pdf/2201.05989) · [DOI 10.1145/3528223.3530127](https://doi.org/10.1145/3528223.3530127) · [arXiv 2201.05989](https://arxiv.org/abs/2201.05989) · [OpenAlex](https://openalex.org/W4221151978)

**Citations:** 4,114 citations (OpenAlex, 2026-10-14) · [239](https://md.research.elamur.ai/free/en/papers/muller-2022-instant-neural-graphics-primitives-multiresolution/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Neural graphics primitives are functions such as images, signed distance fields, radiance caches, or radiance fields, stored in fully connected networks. They tend to be slow to train and query because a large MLP must do most of the work. Müller et al. propose a multiresolution hash encoding to fix this. Each input coordinate is looked up in several grids of increasing resolution. Every grid level is backed by a fixed-size table of trainable feature vectors. Coarse levels map grid points directly to entries, while fine levels share entries through a spatial hash. The interpolated features from all levels are concatenated and fed to a much smaller MLP. Hash collisions are not resolved explicitly. The multiresolution structure and the network learn to work around them, and gradients from important regions naturally dominate. The whole pipeline runs as fully-fused CUDA kernels. The same encoding and hyperparameters work across four tasks: gigapixel images, SDF, NRC and NeRF. High-quality results arrive within seconds of training on a single GPU, and rendering at 1920×1080 takes tens of milliseconds. This makes neural representations practical for interactive and online use.

## Key points
- The encoding has essentially two knobs: the table size 𝑇 (number of parameters) and the finest resolution 𝑁_max. Across tasks, only the hash table size was varied, trading quality against speed.
- In a NeRF comparison at 11,000 steps, the hash encoding was compared with the frequency encoding (438k parameters, 12:45, PSNR 22.90):
  - With 𝑇 = 2^14 (10k MLP + 494k encoding parameters), it trained in 1:48 for PSNR 22.61, over 8× faster.
  - With 𝑇 = 2^19 (12.6M encoding parameters), it reached PSNR 24.58 in 1:47.
- A dense 128³ grid of 16-dimensional features needs 33.6M parameters, yet only 53,807 cells (2.57%) touch the visible surface. This waste motivates the sparse, hashed design.
- Lookups are O(1), contain no control flow, and can be done in parallel for all levels. This avoids the pointer-chasing and divergence that tree structures cause on GPUs.
- The authors tested alternative hash functions: PCG32, space-filling-curve ordering, and dense tiling. None beat the chosen simple hash once both quality and speed were considered.
- The main remaining artifact is grainy microstructure on learned SDFs, which comes from collisions the MLP cannot fully compensate for.

## Interesting ideas
- **Let collisions be resolved by learning.** Instead of building collision-free or adaptively pruned structures, the authors accept aliasing in a fixed-size table and rely on gradient averaging to favor important regions. This could be reused for any large sparse embedding space, such as hashed n-gram or geographic-cell embeddings with bounded memory.
- **Use a multiresolution stack to disambiguate.** Coarse levels are collision-free and fine levels are hashed, so the combination of levels identifies a location even when single levels collide. Layering cheap, imperfect lookups at several scales is a general trick for compact representations.
- **Shift capacity from the network to a sparse lookup.** Moving parameters into a table where each sample touches only a few entries keeps the cost per update low even when the total parameter count is large. This is worth considering wherever training speed matters more than memory.
- **Concatenate features by default.** Concatenating per-level features (with 𝐹 = 2) beat summing them. It keeps levels independent and parallel, and it preserves information. This is a useful default when fusing multi-scale features, though the authors note that reduction can pay off when the downstream network dominates cost.
- **Report parameter counts, time and quality together.** The comparison figure lists MLP and encoding parameters separately alongside wall-clock time and PSNR. This makes trade-offs between encodings transparent, and the same evaluation format would suit model comparisons in other fields.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Thomas Muller, Alex Evans, Christoph Schied and Alexander Keller. 2022. Instant Neural Graphics Primitives with a Multiresolution Hash Encoding. arXiv:2201.05989 · ACM Trans. Graph. 41, 4, Article 102 (July 2022), 15 pages.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{muller2022instant,
  title = {{Instant Neural Graphics Primitives with a Multiresolution Hash Encoding}},
  author = {Thomas Muller, Alex Evans, Christoph Schied and Alexander Keller},
  year = {2022},
  doi = {10.1145/3528223.3530127},
  eprint = {2201.05989},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1145/3528223.3530127}
}
```

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*Updated 2 November 2026*