# NeuroHex: A Brain-Inspired Hex Coordinate System to Enable Highly Computationally-Efficient World Models for Continuous Online-Adaptive Learning

arXiv: https://arxiv.org/abs/2603.00376 · HTML: https://mlsanity.com/paper/2603.00376/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for navigation, one of 11 directions in World models.
- Builds on 2 of its 33 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Placed in

- World models / [World models for navigation](https://mlsanity.com/wm/world-models-for-navigation/)

## Builds on (most cited first, 2 of 2)

- [Toward Next-Generation Artificial Intelligence: Catalyzing the NeuroAI Revolution](https://mlsanity.com/paper/2210.08340/) (2022)
- [World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challenges](https://mlsanity.com/paper/2301.05832/) (2023)

## Abstract (arXiv)

NeuroHex is a brain-inspired hexagonal coordinate system designed to support highly efficient world models and reference frames for online adaptive AI systems. Inspired by the hexadirectional firing structure of grid cells in the human brain, NeuroHex adopts a cubic isometric hexagonal coordinate formulation that provides full 60deg rotational symmetry and low-cost translation, rotation and distance computation. We develop a mathematical framework that incorporates ring indexing, quantized angular encoding, and a hierarchical library of foundational, simple, and complex geometric shape primitives. These constructs allow low-overhead point-in-shape tests and spatial matching operations that are expensive in Cartesian coordinate systems. To support realistic settings, we also develop a novel tool (OSM2Hex) that can process OpenStreetMap (OSM) data sets and convert them into the NeuroHex coordinate system. The OSM2Hex spatial abstraction processing pipeline can achieve a reduction of 90-99% in geometric complexity while maintaining the relevant spatial structure map for navigation. Our initial results, based on actual city and neighborhood scale data sets, demonstrate that NeuroHex offers a highly efficient substrate for building dynamic world models to enable adaptive spatial reasoning in autonomous energy-efficient AI systems with continuous online-adaptive learning (COAL) capability.