Resonant neuronal groups

We create a Spiking Neural Network (SNN) architecture based on transforming the dynamics – Unstable Periodic Orbits (UPOs) – of a chaotic spiking neuron model to Neuronal Groups composed from Resonant Neurons. An input fed to the SNN will activate one of its neuronal groups. An activated neuronal group represents ‘memory’ or a neural state of the SNN. By exploiting a fundamental principle in chaos theory, which is Chaotic Sensitivity upon Initial Conditions, in conjunction with chaos control, we show that similar inputs, when fed separately to the SNN, will always activate the same neuronal group and different inputs will activate different neuronal groups. In addition, we show that differences between the system responses (i.e. neuronal groups) are proportional to differences between inputs. These features make the system suitable for input discrimination; we give an example of discerning human physical actions. More importantly, we study the capacity of the SNN. We show that the number of neuronal groups that can be reached is extremely large; it grows exponentially with the increase of the network size (i.e. number of neurons). This is due to neurons mixing, which allows the same resonant neuron to belong to other neuronal groups and due to the theoretically infinite number of UPOs available in a chaotic system that can be stabilized through chaos control. Also, our work competes with Izhikevich's polychronous groups, so we compare our results to his. We discuss the relevance of the work in the nonlinear sciences and its relation to chaotic neuro-dynamics, cognitive science, neural computation, machine learning and memory modeling including future considerations and open problems.