用随机游走核建模海马体位置细胞，实现多尺度空间导航。
Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning
- 通过多步随机游走转移核的谱分解，构建非负空间嵌入。
- 嵌入内积反映位置间转移概率相似性，形成连通认知地图。
- 自然生成稀疏放电场与θ相位，适合神经机制研究者。
海马体通过位置细胞群体活动编码认知地图以支持空间导航。本文将位置细胞群建模为多步随机游走转移核谱分解所得的非负空间嵌入。嵌入间的内积或等价的欧氏距离编码了不同位置在多尺度转移概率上的相似性，构成邻接关系的认知地图。非负性与内积结构自然诱导稀疏性，无需显式约束即可解释位置细胞局部放电场的形成。定义扩散尺度的时间参数同时决定放电场大小，符合海马背腹梯度结构。该方法通过局部转移的递归组合高效构建全局表征，实现平滑、无陷阱的路径规划及类似预放电的轨迹生成。此外，θ相位内在地表现为嵌入间的角关系，将空间与时间编码统一于同一几何表示中。
原文摘要 · Abstract (English)
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels. In this framework, inner product or equivalently Euclidean distance between embeddings encode similarity between locations in terms of their transition probability across multiple scales, forming a cognitive map of adjacency. The combination of non-negativity and inner-product structure naturally induces sparsity, providing a principled explanation for the localized firing fields of place cells without imposing explicit constraints. The temporal parameter that defines the diffusion scale also determines field size, aligning with the hippocampal dorsoventral hierarchy. Our approach constructs global representations efficiently through recursive composition of local transitions, enabling smooth, trap-free navigation and preplay-like trajectory generation. Moreover, theta phase arises intrinsically as the angular relation between embeddings, linking spatial and temporal coding within a single representational geometry.
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