Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation

2026-09-04

AI Summary

研究提出BCM方法，通过自监督Bellman目标和紧凑坐标编码解决成本感知导航问题，实现高效存储与复杂环境下的可扩展性。

Abstract

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.

Problem

• cognitive map
• navigation
• memory efficiency
• route costs

Innovation

• Bellman-grounded
• compact coordinate encoding
• cost-aware navigation
• reusable cognitive map
• sublinear memory growth