Minimal Neuron Circuits -- Part I: Resonators

Spiking Neural Networks have earned increased recognition in recent years owing to their biological plausibility and event-driven computation. Spiking neurons are the fundamental building components of Spiking Neural Networks. Those neurons act as computational units that determine the decision to fire an action potential. This work presents a methodology to implement biologically plausible yet scalable spiking neurons in hardware. We show that it is more efficient to design neurons that mimic the $I_{Na,p}+I_{K}$ model rather than the more complicated Hodgkin-Huxley model. We demonstrate our methodology by presenting eleven novel minimal spiking neuron circuits in Parts I and II of the paper. We categorize the neuron circuits presented into two types: Resonators and Integrators. We discuss the methodology employed in designing neurons of the resonator type in Part I, while we discuss neurons of the integrator type in Part II. In part I, we postulate that Sodium channels exhibit type-N negative differential resistance. Consequently, we present three novel minimal neuron circuits that use type-N negative differential resistance circuits or devices as the Sodium channel. Nevertheless, the aim of the paper is not to present a set of minimal neuron circuits but rather the methodology utilized to construct those circuits.