用类脑六边形坐标系，让AI高效构建动态世界模型。
NeuroHex: A Brain-Inspired Hex Coordinate System to Enable Highly Computationally-Efficient World Models for Continuous Online-Adaptive Learning
- 模仿大脑网格细胞，用六边形坐标实现低开销空间计算。
- 处理地图数据时几何复杂度降低90%-99%，保留导航结构。
- 适合需要持续学习的节能型自主系统，如机器人导航。
NeuroHex 是一种受大脑启发的六边形坐标系统，旨在支持高效的世界模型与参考框架，适用于在线自适应人工智能系统。它借鉴人类大脑中网格细胞的六向放电结构，采用立方等距六边形坐标形式，实现完整的60°旋转对称性，并具备低成本的平移、旋转与距离计算能力。我们构建了包含环索引、量化角度编码及基础几何形状基元库的数学框架，使点在形状内检测和空间匹配等操作在六边形系统中开销极低，而这些操作在笛卡尔坐标系中代价高昂。为支持真实场景，我们开发了新工具 OSM2Hex，可将 OpenStreetMap (OSM) 数据转换为 NeuroHex 坐标系统。该空间抽象处理流程在保持导航相关空间结构的前提下，将几何复杂度降低90%至99%。基于实际城市与社区尺度数据集的初步结果表明，NeuroHex 为构建动态世界模型提供了高效率底座，可支撑具有连续在线自适应学习（COAL）能力的自主、节能型AI系统进行自适应空间推理。
原文摘要 · Abstract (English)
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° 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.
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