PEPS: Positional Encoding Projected Sampling -- Extended

2026-04-27

AI Summary

This work addresses the limited expressivity of positional encoding in conventional implicit neural representations and the high-resolution requirements of existing grid-based encodings for effective learning. The authors introduce a novel approach that models positional encoding as a series of projected points governed by specific motion patterns across different frequencies. Building upon this formulation, they propose a basis decomposition strategy to construct a learnable, grid-based positional encoding scheme. The method consistently outperforms state-of-the-art techniques across multiple tasks—including image representation, texture compression, and signed distance function modeling—achieving comparable or superior reconstruction and rendering accuracy with approximately 25% fewer parameters.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Implicit Neural Representations
• Positional Encoding
• Grid Encoding
• Coordinate Encoding
• Parameter Efficiency

Innovation

• Positional Encoding
• Implicit Neural Representations
• Projected Sampling
• Learned Encoding
• Neural Fields