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

TL;DR

NeuroHex introduces a brain-inspired hexagonal coordinate system that enables efficient world modeling and spatial reasoning for adaptive AI, inspired by grid cell structures in the human brain.

Contribution

The paper presents a novel cubic isometric hexagonal coordinate framework and a processing pipeline that significantly reduces geometric complexity for online adaptive AI systems.

Findings

Achieves 90-99% reduction in geometric complexity using OSM2Hex.

Supports low-overhead point-in-shape tests and spatial matching operations.

Demonstrates effectiveness on city-scale spatial data for autonomous navigation.

Abstract

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 60{\deg} 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.