Beyond Positional Encoding: A 5D Spatio-Directional Hash Encoding

2026-03-05

AI Summary

Existing learnable encodings often introduce distortions, singularities, and discontinuities in the directional domain, hindering efficient representation of full-frequency spatial-directional signals. This work proposes the first extension of hash-grid encoding to the directional domain by introducing a five-dimensional spatial-directional joint hash encoding. The approach leverages hierarchical geodesic grids to discretize directions in a singularity-free and continuous manner, with each vertex storing learnable latent variables that drive a neural network. This formulation enables a compact and highly efficient representation of full-frequency signals across both spatial and directional domains. Evaluated on neural path guiding tasks, the method reduces variance by up to a factor of two compared to existing hash encoding schemes under identical sampling budgets, significantly improving rendering quality and convergence efficiency.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

In this work, we propose a new spatio-directional neural encoding that is compact and efficient, and supports all-frequency signals in both space and direction. Current learnable encodings focus on Cartesian orthonormal spaces, which have been shown to be useful for representing high-frequency signals in the spatial domain. However, directly applying these encodings in the directional domain results in distortions, singularities, and discontinuities. As a result, most related works have used more traditional encodings for the directional domain, which lack the expressivity of learnable neural encodings. We address this by proposing a new angular encoding that generalizes the hash-grid approach from proach from M\"uller et al. [2022] to the directional domain by encoding directions using a hierarchical geodesic grid. Each vertex in the geodesic grid stores a learnable latent parameter, which is used to feed a neural network. Armed with this directional encoding, we propose a five-dimensional encoding for spatio-directional signals. We demonstrate that both encodings significantly outperform other hash-based alternatives. We apply our five-dimensional encoding in the context of neural path guiding, outperforming the state of the art by up to a factor of 2 in terms of variance reduction for the same number of samples.

Problem

• spatio-directional encoding
• directional domain
• neural encoding
• hash encoding
• high-frequency signals

Innovation

• spatio-directional encoding
• hash encoding
• geodesic grid
• neural rendering
• directional encoding