# Compact Bellman-Grounded Cognitive Maps for Cost-Aware Navigation

arXiv: https://arxiv.org/abs/2609.05104 · HTML: https://mlsanity.com/paper/2609.05104/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Eigenoption Discovery through the Deep Successor Representation](https://mlsanity.com/paper/1710.11089/) (2017)
- [The Laplacian in RL: Learning Representations with Efficient Approximations](https://mlsanity.com/paper/1810.04586/) (2018)
- [Path Planning using Neural A* Search](https://mlsanity.com/paper/2009.07476/) (2020)
- [Plan2Vec: Unsupervised Representation Learning by Latent Plans](https://mlsanity.com/paper/2005.03648/) (2020)
- [Scaling up and Stabilizing Differentiable Planning with Implicit Differentiation](https://mlsanity.com/paper/2210.13542/) (2022)

## Abstract (arXiv)

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.