One-shot learning of paired association navigation with biologically plausible schemas

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.

The mammalian brain, most extensively studied in rodents and bats, solves an enormous variety of non-spatial cognitive tasks using neural circuitry, including grid cells, place cells, and hippocampal indexing, that originally evolved for physical navigation. We formalize the above observation within the local Urysohn width (LUW) framework for continual learning. The central construct is the metric slingshot: a learned embedding $φ: X \to Z$ that maps an arbitrary learning problem into a navigational latent space $Z$ where pre-evolved contraction maps (grid cells) already provide the metric machinery, so that only the topological indexing subproblem must be solved de novo. We prove three results. First, the optimal spacing of multi-scale grid cell modules is a geometric series whose ratio is determined by the $Ω(w \log w)$ sample complexity bound of the LUW framework; for ecologically plausible parameters, optimality yields $r^* \approx 1.4$--$1.7$, matching electrophysiological measurements in rodent medial entorhinal cortex. Second, the slingshot preserves the width hierarchy with a Lipschitz-controlled transfer bound: a contractive embedding into a fine-resolution navigational space reduces the effective number of contexts the learner must discover. Third, the anatomical separation of the ventral (what'') and dorsal (where'') visual streams achieves the structural decoupling required by Metric-Topology Factorization (MTF) by architecture, without gradient-routing mechanisms. We demonstrate that such metric slingshot is applicable to both perception cognition and motor control. Together, these results provide a unified, complexity-theoretic account of navigation in non-spatial domain, grid cell multi-modularity, and hippocampal-neocortical complementary learning as consequences of a single exaptation principle: metric slingshot.

Insect neuroethology provides a compelling biological template for efficient autonomous navigation. We draw an analogy between the formal embodied AI visual point-goal navigation task and the ability of insects to discover, learn, and refine visually guided paths around obstacles between a discovered food location and their nest. We develop a novel integrative model of mushroom body and central complex, two insect brain structures, that have been implicated, respectively, in associative learning and path integration. We demonstrate the mushroom body learning triggered by collisions results in adaptive obstacle avoidance and consequently optimised paths to the goal, corroborating the hypothesis of recent behavioural work that an insect can learn continuously as they travel. The embodied insect-inspired model achieves success rates comparable to recent state-of-the-art models at many orders of magnitude less computational cost in the standardised Habitat point-goal navigation benchmark. Testing in a more realistic simulated environment validates its robustness to perturbations.