受网格细胞启发，构建可处理空间与抽象关系的向量代数模型
A Grid Cell-Inspired Structured Vector Algebra for Cognitive Maps
- 基于神经模块的3D结构编码，模拟网格细胞的空间特性
- 在路径追踪、时空查询和家族树推理任务中表现优异
- 适合对神经符号计算与认知建模感兴趣的读者
海马-内嗅皮层系统是哺乳动物导航的核心，通过网格细胞编码物理与抽象空间。尽管连续吸引子网络（CANs）能有效模拟物理空间中的网格细胞，但将连续空间与抽象空间计算统一建模仍具挑战。本文提出一种受CAN和向量符号架构（VSAs）启发的新型网格细胞向量符号架构（GC-VSA）模型，采用三维神经模块结构，模拟网格细胞的离散尺度与方向，复现其特征性的六边形感受野。实验表明，该模型在多项任务中具备多功能性：（1）实现精准的路径积分以追踪位置；（2）支持时空表示，用于查询物体位置与时间关系；（3）利用家族树作为结构化测试案例，完成层次关系的符号推理。
原文摘要 · Abstract (English)
The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells. This system is well-studied in neuroscience, and its efficiency and versatility make it attractive for applications in robotics and machine learning. While continuous attractor networks (CANs) successfully model entorhinal grid cells for encoding physical space, integrating both continuous spatial and abstract spatial computations into a unified framework remains challenging. Here, we attempt to bridge this gap by proposing a mechanistic model for versatile information processing in the entorhinal-hippocampal formation inspired by CANs and Vector Symbolic Architectures (VSAs), a neuro-symbolic computing framework. The novel grid-cell VSA (GC-VSA) model employs a spatially structured encoding scheme with 3D neuronal modules mimicking the discrete scales and orientations of grid cell modules, reproducing their characteristic hexagonal receptive fields. In experiments, the model demonstrates versatility in spatial and abstract tasks: (1) accurate path integration for tracking locations, (2) spatio-temporal representation for querying object locations and temporal relations, and (3) symbolic reasoning using family trees as a structured test case for hierarchical relationships.
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