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Scale-Free Navigational Planning by Neuronal Traveling Waves.

Khajeh-Alijani A, Urbanczik R, Senn W - PLoS ONE (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, University of Bern, Bern, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus

Planning in complex environments.(a) Propagated wave of activity from the goal at (1,1) through a 20 × 20 network with obstacles (black bars) is demonstrated in space-space color coded plot of firing times relative to the goal neuron. The intrinsic frequency of the goal neuron is 18 Hz. (b, c) Two examples of navigation path (blue lines) in the network from different start positions (•) to the same goal (◂) such that a slight shift of the starting position implies an entirely different shortest path. The input to the planning layer is  = 12.5 and μext = 12 and the noise level is σext = 0.7. The planning time takes 1 s and readout time is 150 ms.
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pone.0127269.g008: Planning in complex environments.(a) Propagated wave of activity from the goal at (1,1) through a 20 × 20 network with obstacles (black bars) is demonstrated in space-space color coded plot of firing times relative to the goal neuron. The intrinsic frequency of the goal neuron is 18 Hz. (b, c) Two examples of navigation path (blue lines) in the network from different start positions (•) to the same goal (◂) such that a slight shift of the starting position implies an entirely different shortest path. The input to the planning layer is = 12.5 and μext = 12 and the noise level is σext = 0.7. The planning time takes 1 s and readout time is 150 ms.

Mentions: To test our network with more challenging problems we considered classical path finding tasks that have also been suggested to rate animal intelligence [24]. Whether our agent finds the shortest path through a narrow hole in an obstacle depends on the size of the hole, and on the level of noise present in the planning network. While for small noise the slippage can be found without problems (Fig 7a), increasing the fluctuations in the external synaptic input to the planning neurons precludes the finding of the shortcut (Fig 7a, 7b). We next wondered whether the network can deal with a moving goal that changes its position while the agent is on its way. This is in fact possible without pausing to wait until the network relaxes to the new steady state. Once in the steady state, a continuous displacement of the goal leads to a continuous adaptation of the firing phases of the individual planning neurons, and a direct path to the moving target is found on the fly without delay (Fig 7c). Such faithful online modifications of the optimal path would be difficult to explain if the direction field were represented by asymmetric connections that are subject to synaptic plasticity obeying its own dynamics (e.g. by anti-STDP, see [12]). Finally, we challenged the network by a complex maze where a slight shift of the starting position implies an entirely different shortest path (Fig 8). Planning times, readout times and performance were as in an open environment.


Scale-Free Navigational Planning by Neuronal Traveling Waves.

Khajeh-Alijani A, Urbanczik R, Senn W - PLoS ONE (2015)

Planning in complex environments.(a) Propagated wave of activity from the goal at (1,1) through a 20 × 20 network with obstacles (black bars) is demonstrated in space-space color coded plot of firing times relative to the goal neuron. The intrinsic frequency of the goal neuron is 18 Hz. (b, c) Two examples of navigation path (blue lines) in the network from different start positions (•) to the same goal (◂) such that a slight shift of the starting position implies an entirely different shortest path. The input to the planning layer is  = 12.5 and μext = 12 and the noise level is σext = 0.7. The planning time takes 1 s and readout time is 150 ms.
© Copyright Policy
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC4497724&req=5

pone.0127269.g008: Planning in complex environments.(a) Propagated wave of activity from the goal at (1,1) through a 20 × 20 network with obstacles (black bars) is demonstrated in space-space color coded plot of firing times relative to the goal neuron. The intrinsic frequency of the goal neuron is 18 Hz. (b, c) Two examples of navigation path (blue lines) in the network from different start positions (•) to the same goal (◂) such that a slight shift of the starting position implies an entirely different shortest path. The input to the planning layer is = 12.5 and μext = 12 and the noise level is σext = 0.7. The planning time takes 1 s and readout time is 150 ms.
Mentions: To test our network with more challenging problems we considered classical path finding tasks that have also been suggested to rate animal intelligence [24]. Whether our agent finds the shortest path through a narrow hole in an obstacle depends on the size of the hole, and on the level of noise present in the planning network. While for small noise the slippage can be found without problems (Fig 7a), increasing the fluctuations in the external synaptic input to the planning neurons precludes the finding of the shortcut (Fig 7a, 7b). We next wondered whether the network can deal with a moving goal that changes its position while the agent is on its way. This is in fact possible without pausing to wait until the network relaxes to the new steady state. Once in the steady state, a continuous displacement of the goal leads to a continuous adaptation of the firing phases of the individual planning neurons, and a direct path to the moving target is found on the fly without delay (Fig 7c). Such faithful online modifications of the optimal path would be difficult to explain if the direction field were represented by asymmetric connections that are subject to synaptic plasticity obeying its own dynamics (e.g. by anti-STDP, see [12]). Finally, we challenged the network by a complex maze where a slight shift of the starting position implies an entirely different shortest path (Fig 8). Planning times, readout times and performance were as in an open environment.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, University of Bern, Bern, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus