Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation

arXiv:2609.05104v1 Announce Type: new 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.

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.

Artificial Intelligence (cs.AI)

arXiv:2609.05104 [cs.AI]

(or arXiv:2609.05104v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.05104 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation

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