Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation
A paper titled 'Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation' was published on arXiv (cs.AI) on 2026-09-04. It introduces BCM, a cognitive-map model grounded in local edge costs via a self-supervised Bellman-grounded objective and compact coordinate encoding. On weighted grids up to N=1600 nodes, BCM maintains full success and 5% mean Gap relative to exact Dijkstra search, versus about 45% for a connectivity-based spectral baseline. Memory footprint grows sublinearly as graph size increases from N=400 to N=3600.
Researchers present BCM, a compact cognitive-map model that grounds reusable navigation maps in additive heterogeneous route costs. BCM supports changing goal queries without per-goal retraining and demonstrates strong performance on weighted grids, achieving full success and only 5% mean Gap versus Dijkstra, compared to 45% for a spectral baseline. Its memory footprint scales sublinearly with environment size, making it suitable for complex environments.
BCM uses a self-supervised Bellman-grounded objective to embed local edge costs into a compact coordinate encoding. This allows the model to reuse a single learned map for multiple goals without retraining, while maintaining near-optimal path costs. The sublinear memory growth suggests efficient representation of large state spaces, a key challenge in cognitive-map models.
This research advances AI navigation and spatial reasoning, potentially benefiting robotics, autonomous systems, and simulation environments where cost-aware path planning is critical. The compact representation could reduce memory and compute requirements in deployed systems.
The method could lower computational costs for navigation in large environments, enabling more scalable autonomous systems. It may be relevant to companies developing robotics, logistics, or game AI where efficient path planning is a differentiator.
Next signals include validation on more complex or real-world environments, integration with reinforcement learning agents, and comparisons with other cost-aware navigation methods. Potential extensions to dynamic costs or continuous spaces may follow.