Source
Four papers, converging from different directions:
- Müller et al. (2022), LIT-064 — a multiresolution hash grid; training in seconds, rendering in tens of milliseconds.
- Kerbl et al. (2023), LIT-108 — anisotropic 3D Gaussians; the first real-time (>=30 fps) radiance-field rendering at 1080p.
- Fridovich-Keil et al. (2023), LIT-086 — planar factorisation, and the one that needs no custom kernels.
- Wang et al. (2023), LIT-109 — the hash-encoding line applied to implicit surfaces rather than radiance fields.
- Zhang et al. (2024), LIT-511 — read as NOTE-256 — 2D Gaussians for a single image, and the first source here outside 3D.
What it costs to decode, measured
The four 3D sources argue the case from rendering speed, which entangles the representation with a rasterizer. LIT-511 gives the number in the units the claim is actually about: 0.3K multiply-accumulates per pixel to decode, against 3K MACs at 0.31 bpp for C3, a neural codec in the same quality range. An order of magnitude, from moving the capacity out of the network.
It also shows the claim is not confined to scenes. A single image has no viewpoint, no occlusion and no geometry to exploit, so it is close to the weakest case for an explicit structure — and the explicit structure still wins against six implicit baselines held at matched model size, across the bitrate range.
The claim
The instinct when a coordinate-queried field is too slow is to make the network smaller or the sampling cheaper. These four do something else: they move the capacity out of the network entirely, into a structure that can be addressed rather than evaluated — a hash table, a set of planes, a set of primitives — and leave a small decoder behind it.
The decoder can then be small because the structure already carries the variation. K-Planes states the strong form: put the structure in the representation and the decoder can be linear. That is the opposite of the usual instinct to add capacity where the output is produced.
Why this is one practice and not four
The three structures are not variants of one method — a hash grid, a plane factorisation and a cloud of Gaussians have almost nothing in common mechanically. What they share is the decision: that for a spatially sparse signal, lookup beats evaluation. Three groups arriving there by different routes within eighteen months is stronger evidence for the decision than any of them is for its own structure.
Conditions
- The signal must be spatially sparse — that is what makes an addressable structure smaller than the network it replaces, and what makes hash collisions survivable: LIT-064 accepts collisions and lets training absorb them rather than building a mechanism to resolve them.
- Something must place the structure. LIT-108 initialises its Gaussians from the sparse points that camera calibration already produced, and ablates that choice as load-bearing. The general form — initialise from structure you already computed — is the practice’s most portable corollary and the record holds one ablation of it.
- Custom kernels are a real cost. LIT-086 makes the point by not needing them; whether a method requires them belongs in its report.
- The quality/cost trade should be exposed as one number. LIT-064’s is hash table size.
Scope
This takes a domain topic under ADR-026 because it is a claim about neural graphics primitives as such: the sparsity it depends on is a property of 3D scenes, and there is no version of it that survives the domain changing. The generalised form — “prefer lookup to evaluation where the signal is sparse” — would be an aphorism, not a practice, and the record does not hold it.
Known implementations
- Instant-NGP, 3D Gaussian Splatting, K-Planes, NeuS2 — and the tooling built on the first two is where most practitioners meet this.