1. Introduction

Computer graphics primitives are represented by mathematical functions→MLPs used as neural graphics primitives e.g NeRF, Neural sparse voxel fileds, deep SDF, ACORN

• The inputs of the neural network needs to be encoded(mapped) in to higher dimensions to extract high approximation quality from compact models
  • [-] heuristic, structural modifications that complicate training→task specific, limit GPU performance
• Multiresolution hash encoding
  • Adaptivity
    • Mapping cascade of grids to fixed size array feature vectors → No structural update needed
    • coarse resolution → 1:1 mapping
    • fine resolution → spatial hash function automatically prioritizing sparse areas with most important fine detail
  • Efficiency
    • $O(1)$ hash tabel lookup
    • No pointer-chasing
  • Independent of task
    • Gigapixel image, Neural SDF, NRC, NeRF

2. Background and Related work

Frequency Encodings

• Transformers introduced encoded scalar positions as a multi resolution sequence of $L \isin \mathbb{N}$ sine and cosine functions

$$ enc(x) = \Bigl( \sin(2^0x),\sin(2^1x),\dots ,\sin(2^{L-1}x), \\ \\cos(2^0x),\cos(2^1x),\dots ,\cos(2^{L-1}x) \Bigr) $$

Parametric Encodings

• Arrange additional trainable parameters in an auxiliary data structure e.g grid, tree and to look-up and interpolate these parameters depending on the input vector.

• Larger memory footprint for a smaller computational cost

  • For each gradient → every parameter in MLP needs to be updated, but for trainable input encoding parameters, only a small number are affected

  reducing the size of the MLP, such parametric models can typically be trained to convergence much faster without sacrificing approximation quality

Coordinate Encoder

• Large Auxiliary coordinate encoder neural network (ACORN) is trained to ouput dense feature grids around $\bold{x}$

Sparse Parametric Encodings

• Dense Grids → Consume much memory, fixed resolution
  • Allocates too much memory on empty space
  • Natural scenes exhibit smoothness → multi resolution decomposition