Encoding of Input Signals in Terms of Path Complexes in Spiking Neural Networks

The article proposes a method for encoding input signals in a spiking neural network based on the mathematics of path complexes on directed graphs. The hypothesis formulated is that when the input signal is repeatedly applied, the STDP dynamics increases synaptic weights along the pathways of active neurons, while the weights of other synaptic connections decrease. As a result, a directed subgraph (path complex) is appearing for each input signal consisting of edges with large synaptic weights. Such path complexes should be unique for different input signals. This hypothesis is confirmed by the example of a simple spiking neural network model, for which a relevant parameter window has been found. Two methods of comparing path complexes (input signals encodings) are proposed. The first one is based on the introduction of the Euclidean metric on a set of path complexes, and the computation of distances between path complexes. The second one consists of compiling the algebra-topological portraits of path complexes—simplexes and homologies, and their subsequent comparison. The proposed method of encoding input signals is, in fact, a new tool that can be considered as an initial stage in the development of a new type of approaches to data analysis.