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文章背景与核心概要

在生物学中，智能体能够利用可重用的认知地图高效地导航环境，而无需为每个新目标重新计算路线。然而，现有的许多人工模型在环境规模扩大时往往面临内存效率低下的问题，并且难以处理异构的路线成本。

本文介绍了 BCM（Bellman-Grounded Cognitive Maps，贝尔曼扎根认知地图） 这一创新方法，该方法通过自监督的贝尔曼扎根目标函数和紧凑的坐标编码，将认知地图扎根于局部边缘成本。BCM 能够针对不断变化的目标实现灵活导航，而无需针对每个目标进行重新训练。在加权网格上的实验结果表明，BCM 实现了接近最优的性能（与 Dijkstra 搜索相比平均差距仅为 5%），同时随着环境规模扩大保持了亚线性的内存占用，从而弥合了生物灵活性与最优路径规划之间的差距。

Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation

Authors: Yuzhe Han, Mingkun Xu, Yujie Wu
Date: September 4, 2026
Subject: Artificial Intelligence (cs.AI)
arXiv ID: 2609.05104

Authors: Yuzhe Han, Mingkun Xu, Yujie Wu
Date: September 4, 2026
Subject: Artificial Intelligence (cs.AI)
arXiv ID: 2609.05104

Summary

Biological agents efficiently navigate environments by utilizing a reusable cognitive map rather than re-calculating routes for every new goal. Existing artificial models often struggle with memory efficiency as environments scale and fail to account for heterogeneous route costs.

This paper introduces BCM (Bellman-Grounded Cognitive Maps), a novel approach that grounds cognitive maps in local edge costs using a self-supervised Bellman-grounded objective and a compact coordinate encoding. BCM enables flexible navigation for changing goals without the need for per-goal retraining. Experimental results on weighted grids demonstrate that BCM achieves near-optimal performance (matching Dijkstra search with only a 5% mean Gap) while maintaining a sublinear memory footprint as the environment scales, bridging the gap between biological flexibility and optimal path planning.

Summary

Biological agents efficiently navigate environments by utilizing a reusable cognitive map rather than re-calculating routes for every new goal. Existing artificial models often struggle with memory efficiency as environments scale and fail to account for heterogeneous route costs.

This paper introduces BCM (Bellman-Grounded Cognitive Maps), a novel approach that grounds cognitive maps in local edge costs using a self-supervised Bellman-grounded objective and a compact coordinate encoding. BCM enables flexible navigation for changing goals without the need for per-goal retraining. Experimental results on weighted grids demonstrate that BCM achieves near-optimal performance (matching Dijkstra search with only a 5% mean Gap) while maintaining a sublinear memory footprint as the environment scales, bridging the gap between biological flexibility and optimal path planning.

Key Contributions

  • Cost-Aware Navigation: Unlike traditional connectivity-based models, BCM explicitly incorporates additive heterogeneous route costs.
  • Memory Efficiency: The model utilizes a compact coordinate encoding that allows the memory footprint to grow sublinearly as the graph size increases (tested up to \(N=3600\) nodes).
  • Scalability & Performance: BCM maintains high success rates and competitive accuracy compared to exact algorithms, even in complex, large-scale environments.
  • Reusable Representation: The map is built once and supports arbitrary goal queries, eliminating the computational overhead of per-goal retraining.

Key Contributions

  • Cost-Aware Navigation: Unlike traditional connectivity-based models, BCM explicitly incorporates additive heterogeneous route costs.
  • Memory Efficiency: The model utilizes a compact coordinate encoding that allows the memory footprint to grow sublinearly as the graph size increases (tested up to \(N=3600\) nodes).
  • Scalability & Performance: BCM maintains high success rates and competitive accuracy compared to exact algorithms, even in complex, large-scale environments.
  • Reusable Representation: The map is built once and supports arbitrary goal queries, eliminating the computational overhead of per-goal retraining.

Technical Metadata

Category Details
Primary Subject Artificial Intelligence (cs.AI)
DOI 10.48550/arXiv.2609.05104
Full-Text PDF | HTML | TeX Source

Technical Metadata

Category Details
Primary Subject Artificial Intelligence (cs.AI)
DOI 10.48550/arXiv.2609.05104
Full-Text PDF | HTML | TeX Source

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