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This study demonstrates how a hippocampal recurrent network can achieve optimal goal-directed navigation through relaxation dynamics, mathematically linking neural activity fields to Linearly-solvable Markov Decision Processes. By modeling transition probabilities as synaptic weights and learning via behavioral-timescale plasticity, the research offers a circuit-level principle for planning in complex environments that remains robust against obstacles. The findings bridge computational neuroscience and AI by showing how biological circuits naturally implement efficient pathfinding strategies relevant to reinforcement learning agents.
Planning as Dynamics Relaxation: Hippocampal Recurrent Network Realizes Optimal Goal-Directed Navigation
arXiv:2609.13219v1 Announce Type: cross Abstract: Neural correlates of spatial cognitive map are well documented, yet exactly how neural circuits perform spatial navigation in complex environments - e.g., reaching a goal while avoiding obstacles - remains largely unclear. Here, we show that a hippocampal network with appropriate recurrent connections can naturally achieve optimal goal-directed navigation via its relaxation dynamics. Specifically, we consider that the recurrent weights between the neurons represent the transition probabilities between spatial locations encoded by neurons; obstacles such as walls and blocked corridors are therefore reflected by the vanishing of connection weights. This connection pattern can be learned in the hippocampus via behavioral-timescale synaptic plasticity (BTSP) while the animal is exploring the environment. When a goal signal is presented, the network dynamics will relax into an activity field representing the goal location. We prove that this field is mathematically equivalent to the desirability field of a Linearly-solvable Markov Decision Process (LMDP), and the local log-gradient of the field indicates the navigation direction. Both theoretical analyses and simulations demonstrate that this recurrent network dynamics-mediated navigation is efficient and robust in environments with complex obstacle layouts. Moreover, only low-rank updates of the network's connection pattern are needed when the environment has local changes. We hope this study offers insight into a general circuit principle for planning in abstract rational maps in the brain beyond spatial navigation.
Abstract:Neural correlates of spatial cognitive map are well documented, yet exactly how neural circuits perform spatial navigation in complex environments - e.g., reaching a goal while avoiding obstacles - remains largely unclear. Here, we show that a hippocampal network with appropriate recurrent connections can naturally achieve optimal goal-directed navigation via its relaxation dynamics. Specifically, we consider that the recurrent weights between the neurons represent the transition probabilities between spatial locations encoded by neurons; obstacles such as walls and blocked corridors are therefore reflected by the vanishing of connection weights. This connection pattern can be learned in the hippocampus via behavioral-timescale synaptic plasticity (BTSP) while the animal is exploring the environment. When a goal signal is presented, the network dynamics will relax into an activity field representing the goal location. We prove that this field is mathematically equivalent to the desirability field of a Linearly-solvable Markov Decision Process (LMDP), and the local log-gradient of the field indicates the navigation direction. Both theoretical analyses and simulations demonstrate that this recurrent network dynamics-mediated navigation is efficient and robust in environments with complex obstacle layouts. Moreover, only low-rank updates of the network's connection pattern are needed when the environment has local changes. We hope this study offers insight into a general circuit principle for planning in abstract rational maps in the brain beyond spatial navigation.
Neurons and Cognition (q-bio.NC); Artificial Intelligence (cs.AI)
arXiv:2609.13219 [q-bio.NC]
(or arXiv:2609.13219v1 [q-bio.NC] for this version)
https://doi.org/10.48550/arXiv.2609.13219 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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