Scale-Free Navigational Planning by Neuronal Traveling Waves

Abstract

Spatial navigation and planning is assumed to involve a cognitive map for evaluating trajectories towards a goal. How such a map is realized in neuronal terms, however, remains elusive. Here we describe a simple and noise-robust neuronal implementation of a path finding algorithm in complex environments. We consider a neuronal map of the environment that supports a traveling wave spreading out from the goal location opposite to direction of the physical movement. At each position of the map, the smallest firing phase between adjacent neurons indicate the shortest direction towards the goal. In contrast to diffusion or single-wave-fronts, local phase differences build up in time at arbitrary distances from the goal, providing a minimal and robust directional information throughout the map. The time needed to reach the steady state represents an estimate of an agent’s waiting time before it heads off to the goal. Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map. In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

A Brain-Inspired Model of Hippocampal Spatial Cognition Based on a Memory-Replay Mechanism

“…Since Huang et al [ 34 ] and Khajeh-Alijani et al [ 33 ] also focused on solving the problem of the attenuation of neuronal signals, similar to our model, there was no need to perform any hierarchical treatment of environmental states, so we chose to compare experiments with their models. Khajeh-Alijani et al designed a complex maze to test the signal transmission strength of the model.…”

“…Khajeh-Alijani et al also focused on the problem of neuronal signal attenuation, and they proposed a phase-encoding scheme that can span multiple spatial scales within a single network, and they demonstrated the navigation of complex mazes. Since their research aimed at similar problems, we will compare our model with that of Khajeh-Alijani et al in navigation experiments in the complex maze they designed to demonstrate the feasibility of our model in complex environments [ 33 ].…”

“…As shown in Figure 21 , Figure 21 a,b are the results of our model navigating in this environment: The red circle represents the starting point, and the green square represents the position of the goal. Figure 21 c,d are the complex maze navigation paths provided by Khajeh-Alijani et al [ 33 ]. It can be seen that our model has fewer bifurcation paths in the navigation process and is more robust in complex environments.…”

“…These models can solve the problem of signal attenuation to some extent, but they need to layer the environmental state; the operation is complex, and there is no unified standard; and there is no commonality. In contrast, Khajeh-A et al [ 33 ] proposed a phase-encoding scheme based on a wave propagation algorithm that allows an agent to perform path planning within a single network across multiple spatial scales without the need for hierarchical coding. Huang et al [ 34 ] proposed a brain-inspired model that combines endogenous and exogenous information and ensures the stable propagation of reward signals by adding an olfactory system to the model and using odor as a stable potential energy field.…”

Endotaxis: A neuromorphic algorithm for mapping, goal-learning, navigation, and patrolling

“…Some key elements of the endotaxis model have appeared in prior work, starting with the notion of ascending a scalar goal signal during navigation [50, 52, 66]. Several models assume the existence of a map layer, in which individual neurons stand for specific places, and the excitatory synapses between neurons represent the connections between those places [23, 33, 39, 47, 53, 65, 66]. Then the agent somehow reads out those connections in order to find the shortest path between its current location (the start node) and a desired target (the end node).…”