Very Small Spiking Neural Networks Evolved for Temporal Pattern Recognition and Robust to Perturbed Neuronal Parameters

The Importance of Self-excitation in Spiking Neural Networks Evolved to Recognize Temporal Patterns

“…We observe that a variety of network topologies resulting from an artificial evolutionary process can perform the same computational task [38][39][40]. This is also the case for biological networks [18,22].…”

“…Each network in our model is encoded in a linear genome, and consists of three inputs, three interneurons, and one output neuron [38][39][40]. Inputs are not allowed to connect to the output neuron directly and only interneurons can have self-loops.…”

“…A fully connected network with this structure can have up to 21 connections (up to nine connections from inputs to interneurons, six connections between the interneurons, three self-loops, and three connections from the interneurons to the output neuron). Each input is dedicated to one signal (stimulus type), denoted as A, B and C. The interneurons and output neuron are modelled using Euler integration with 1 ms steps of the differential equations for adaptive exponential integrate and fire neurons [20]; we use the same parameter values as in [38][39][40]; these values result in tonic spiking in response to constant input current. Since this study focuses on the effect of network connectivity, the neuronal parameters are kept constant (allowing them to evolve would hugely increase the search space of the artificial evolutionary process).…”

“…The task of the networks is to recognize three signals in a particular order (ABC) in a continuous random sequence (...BCACACCABCACBAC...), in which all signals appear with equal probability, and thus the correct patterns take up about 10% of time. To generate a variety of solutions, we use a genetic algorithm with a population of 300 individuals, with 100 independent runs for each of the two settings: in the first setting signals are followed by a constant interval of silence (16 ms), in the second setting the intervals vary, with a uniform distribution between 16 and 32 ms (in previous work, [38,40], we used noise on the membrane potential, but did not vary the interval of silences). In both settings the length of a each signal is 6 ms. We use the same genetic operators as in [40]; they can result in changes of weights, deletion and addition of edges (synapses) and the nodes (neurons) in the network (through deletion and duplication, respectively, of consecutive elements in the linear genomes; however, the maximum size of the network was limited as described above).…”

“…We have shown previously that without noise, two interneurons are sufficient for this task, but such networks are fragile to even the slightest variation of the timing of inputs [39]. In contrast, networks with three interneurons can be evolved to recognize patterns consisting of three stimuli in the presence of noise, and they are robust to a change of neuronal parameters or duration of intervals of silence between the stimuli [38,40]. In this work, we use the same model of noise (on the membrane voltage) as previously; while its level is biologically realistic, and so including it adds to the biological plausibility of our model, our primary concern is to aid in the evolution of networks that can maintain their states (a form of memory) even as the intervals between stimuli are hugely increased when testing the evolved network.…”