Rapid, parallel path planning by propagating wavefronts of spiking neural activity

Abstract

Efficient path planning and navigation is critical for animals, robotics, logistics and transportation. We study a model in which spatial navigation problems can rapidly be solved in the brain by parallel mental exploration of alternative routes using propagating waves of neural activity. A wave of spiking activity propagates through a hippocampus-like network, altering the synaptic connectivity. The resulting vector field of synaptic change then guides a simulated animal to the appropriate selected target locations. We demonstrate that the navigation problem can be solved using realistic, local synaptic plasticity rules during a single passage of a wavefront. Our model can find optimal solutions for competing possible targets or learn and navigate in multiple environments. The model provides a hypothesis on the possible computational mechanisms for optimal path planning in the brain, at the same time it is useful for neuromorphic implementations, where the parallelism of information processing proposed here can fully be harnessed in hardware.

Keywords: hippocampus; mental exploration; navigation; neuromorphic systems; parallel processing; path planning; spike timing dependent plasticity; wave propagation.

Figure 1

Synaptic vector field formation. (A,B) Illustration of the synaptic strength changes in a one-dimensional network altered by “causal” STDP (A) and “anti-causal” STDP (B) after a neural activity was propagated from the neuron k in the directions denoted by the arrows. The connections are shown as arcs with the direction of connection denoted by little dots representing synapses. Stronger connections are represented by the thicker lines. Left panels are the schematic illustrations of the synaptic weight changes Δw as a function of the time lag Δt between the post and presynaptic spikes, for STDP (A) and anti-STDP (B). (C) Due to the asymmetry in the strength of connection from- and to- any particular neuron in the network, the mean neural activity observed in the network is shifted with respect to the input current distribution.

Figure 2

Wavefront propagation and neuronal adaptation. Illustration of a wavefront propagation in a network of synaptically connected place cells for two different environments (A,B). Cyan fields are the initiation points of the wavefronts. Red dots are the action potentials that occurred in a time window of 0.002 s centered at the times indicated. Plots (C,D) show color maps of the average level of a neural adaptation in the particular regions of the network after a single wavefront passage up to the states illustrated in the right-far plots in (A,B), respectively. Brighter colors in these maps represent lower excitability of the neurons at the corresponding locations.

Figure 3

Synaptic vector field and spatial navigation. (A,B) Synaptic vector fields resulting from the wavefront initiated at point T and propagated as illustrated in Figures 2A,B, respectively. (C,D) The insets show details of the vector fields around the bifurcations in the simulated mazes. (E,F) Typical movement trajectories observed in the considered models resulting from the vector fields from (A,B), respectively. The trajectories begin in points “S” and end in the target locations “T.” For additional results see also Movie S1 in supplementary materials.

Figure 4

Navigation in a system with multiple targets. (A) Synaptic vector field created in the network with targets in locations Tl, T2, T3. (B) Typical movement trajectories observed in the system for the initial agent locations as indicated by spots Sl, S2, S3. The path selection and the path shapes are determined by the shape of the vector field and by the initial agent location's. The vector field has three basins of attraction corresponding to the particular targets—the bounds of the basins of attraction are indicated by the gray dotted lines. For additional results see also Movie S2 in supplementary materials.

Figure 5

Effects of noise on wavefront propagation. (A) A single wavefront is initially started from the point T. Noise results in spurious single spikes or missing spikes. When spurious spikes cluster, they can serve as initiation sites for new circular waves centered at locations where there is no target. In addition, spurious and absent spikes cause irregular wavefront propagation or even wavefront extinction as illustrated in (B,C). Network activity shown at times as indicated. The noise is modeled by injecting spike currents to randomly selected neurons at random time steps.

Figure 6

Synaptic vector field formation in multiple environments. (A, left) Wavefront propagation in environment “A” short time after the activity wave initiation at the target T. (A, right) The same activity pattern as in (A, left), but displayed in the “∞” environment plotting representation. (B, left) Synaptic vector field resulting from the propagation of a wavefront illustrated in (A, left). Note a single attractor corresponding to the location T, that is the center of the wavefront. (B, right) The synapse vector field due to the same synapse changes as in (B, left), but calculated using the positions of the neurons in the “∞” environment. (C,D) The same plots as for (A,B) except that the wavefront has been initiated at target T in the “∞” environment. All results are qualitatively like those in (A,B), except that the roles of the two environments are reversed. Synaptic vector fields in plots (B,D) are visualized using the same normalization factor (arrow scale) for both environments.

Figure 7

Navigation in multiple environments. Sample movement trajectories in the environment “A” (left panel) and “∞” (right panel) resulting from the synaptic vector fields shown in (left) and (right), respectively. Three different trials for each environment are illustrated. The trajectories start in the S locations and end in the T locations.

Figure 8

lllustration of the supralinear and linear summation. The supralinear function is given by Equation 3. The linear summation function is defined by: i_syn(t) = Σ_j w_ji_j(t). Here, for the supralinear function we took a_syn = 10, b_syn = 0.05, and for both functions we assumed w_ji_j(t) = 1 for all j.