# PEPS: Positional Encoding Projected Sampling -- Extended

arXiv: https://arxiv.org/abs/2604.24167 · HTML: https://mlsanity.com/paper/2604.24167/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Random-Access Neural Compression of Material Textures](https://mlsanity.com/paper/2305.17105/) (2023)
- [Hardware Accelerated Neural Block Texture Compression with Cooperative Vectors](https://mlsanity.com/paper/2506.06040/) (2025)
- [Real-Time Neural Materials using Block-Compressed Features](https://mlsanity.com/paper/2311.16121/) (2023)
- [Local Positional Encoding for Multi-Layer Perceptrons](https://mlsanity.com/paper/2309.15101/) (2023)
- [Neural Graphics Texture Compression Supporting Random Access](https://mlsanity.com/paper/2407.00021/) (2024)
- [Neural Texture Block Compression](https://mlsanity.com/paper/2407.09543/) (2024)

## Abstract (arXiv)

Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on using high-dimensional projections of the initial coordinates through encoders such as grid or positional encoding. Nevertheless, positional encoding is often insufficient and grids, as we show in this paper, require high resolution for being able to learn. In this paper, we demonstrate that positional encoding can be used not only as a high-dimensional embedding but also decomposed as a series of meaningful points. We propose the Positional Encoding Projected Sampling, where we treat the projection of the original coordinate at each frequency as a point of interest. We describe the motion of each point with respect to the frequencies and show that it follows a unique pattern. Finally, we use the unique motion of each point as a basis decomposition for doing learned positional encoding using grids. We prove, using three competitive applications; image representation, texture compression, and signed distance function; that the proposed approach outperforms the current state of the art methods, and often requires 25% less parameters for equivalent reconstruction error or rendering.