发表机构
Guangdong Institute of Intelligence Science and Technology (GDIIST); The Hong Kong Polytechnic University（广东省智能科学与技术研究院; 香港理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出BCM，一种基于贝尔曼目标与紧凑坐标编码的认知地图模型，可复用且无需逐目标重训，在加权网格上内存次线性增长，性能优于基线，弥合生物导航灵活性与最优路径规划的差距。
AI 中文摘要
生物智能体在熟悉环境中导航时，并非为每个新目标重新规划路线，而是复用一次学习得到的地图，随目标变化直接调取。现有人工认知地图模型虽模仿了这种复用能力，但其指导并未明确基于加性异质路线成本，且常存在内存效率问题：代表性的状态索引和高秩谱构造会随环境规模扩大产生大量存储增长。我们提出BCM，该模型通过自监督贝尔曼基础目标函数和紧凑坐标编码，将可复用认知地图建立在局部边成本基础上，支持随目标变化查询而无需针对每个目标重新训练。在最多含N=1600个节点的加权网格上，BCM保持完全的成功率，且相对于精确Dijkstra搜索的平均Gap仅为5%，而基于连通性的谱基线的平均Gap约为45%。值得注意的是，当图规模从N=400增加到N=3600时，其内存占用呈次线性增长，同时保持有竞争力的性能，使我们的方法可扩展到复杂环境。这些结果共同表明，加性路线成本可被写入紧凑、可复用的认知地图表示中，弥合了生物灵活性与最优路径规划之间的差距。
英文摘要
Biological agents navigate familiar environments not by re-solving routes for each new goal, but by reusing a learned map built once and read off as goals change. Existing artificial cognitive-map models mimic this reuse, yet their guidance is not explicitly grounded in additive heterogeneous route costs. Furthermore, they often struggle with memory efficiency: representative state-indexed and high-rank spectral constructions incur substantial storage growth as the environment scales. We present BCM, which grounds a reusable cognitive map in local edge costs through a self-supervised Bellman-grounded objective and a compact coordinate encoding, supporting changing goal queries without per-goal retraining. On weighted grids of up to $N=1600$ nodes, BCM maintains full success and only a 5\% mean Gap relative to exact Dijkstra search, compared with about $45\%$ for a connectivity-based spectral baseline. Notably, as the graph size increases from $N=400$ to $N=3600$, its memory footprint grows sublinearly while maintaining competitive performance, making our method scalable to complex environments. Together, these results show that additive route costs can be written into a compact, reusable cognitive-map representation, bridging the gap between biological flexibility and optimal path planning.
