Figure 2
From: Adaptive nodes enrich nonlinear cooperative learning beyond traditional adaptation by links
Different stationary firing patterns and weights for learning by links and nodes in a feedforward network. (a) A schema of a perceptron with three input units, connected to one output unit with weights and delays (w, τ, color coded). The relative change in the strength of a weight during a learning step is δW (defined in c). The dynamics of each unit is governed by leaky integrated-and-fire neuron (Methods). (b) The same perceptron and delays as in a but the first input is connected to the output node via the left-dendrite, while the two other inputs are connected via the right-dendrite. The dendritic weights and their relative changes during a learning step are denoted by WD and δW, respectively. The initial weights for both dendrites are WD = 1. (c) Left: A typical profile for δW = 0.05*exp(−|Δ|/15)*sign(Δ) during a learning step, where Δ stands for the time-lag between a spike and a sub-threshold stimulation, measured in ms. Right: Scenarios for positive/negative Δ, spikes colored in orange and sub-threshold stimulations are denoted by (green and red) hills. (d) An example of the initial three weights (color coded), where the input units are simultaneously stimulated at 10 Hz. Left: The dynamical evolution of the three weights in a (bottom) and the firing timings of the output unit (dots at upper part), colored following the origin of the above-threshold stimulation. Right: Results for b where initially WD = 1. (e) Similar to d but with different initial weights. The stationary firing patterns in d and e are the same for synaptic learning in a, but differ for dendritic learning in b.
