Minimal Neuron Circuits -- Part I: Resonators (2506.02341v1)

Abstract: 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.

• The paper introduces a minimalist INa,p+IK model that simplifies spiking neuron circuits while maintaining biological plausibility.
• It demonstrates the use of NNDR devices in FET-based resonators to achieve subthreshold oscillations and sustained spiking behavior.
• The research highlights a methodology that enhances hardware scalability and bridges the gap between electronic circuits and natural neuronal dynamics.

Minimal Neuron Circuits -- Part I: Resonators

Introduction

The paper is centered on the development and design methodology of spiking neuron circuits, which are integral components of Spiking Neural Networks (SNNs). The focus is on creating circuits that are both biologically plausible and scalable for hardware implementation. The approach advocates the use of the INa,p+IK model over the traditional Hodgkin-Huxley (HH) model due to its reduced complexity and comparable biological plausibility. This minimalist approach in design is aimed at achieving efficient neuron circuits that replicate the biological dynamics observed in natural neuronal systems as closely as possible while maintaining scalability and component simplicity.

Minimal Neuron Models

The INa,p+IK model simplifies the neuron representation by reducing the system to two coupled ordinary differential equations, contrasting with the four-equation HH model. The model emulates the dynamics of neuronal ion channels, focusing on sodium and potassium channels' behavior to manifest action potentials. The model's dynamics are characterized by the quick activation of sodium channels and slower potassium channels, leading to distinct neuronal firing mechanisms. The paper outlines the use of NNDR circuits or devices to imitate sodium channels, a strategy that leverages the biologically inspired properties of type-N negative differential resistance.

FET-Based Minimal Neuron (Resonator)

One of the proposed circuits utilizes a combination of MOSFETs and capacitors to achieve a resonator-type minimal neuron circuit. The circuit demonstrates subthreshold oscillations and sustained spiking behavior akin to the biological mechanisms illustrated by the INa,p+IK model. The neuronal firing process in this circuit involves an intricate interplay between the sodium and potassium channels, facilitating the emergence of action potentials leveraging the positive feedback from NNDR circuits. The circuit is carefully designed to ensure the NNDR component operates within its negative differential resistance region, thus enhancing the circuit's excitability and responsiveness to input stimuli.

Other Minimal Neurons (Resonators)

Beyond the FET-based resonator, the paper introduces additional minimalist neuron circuits utilizing different NNDR device options, including those based on JFETs and unipolar memristors. These circuits further underscore the versatility of NNDR properties in emulating sodium channels within neuron models, like the INa,p+IK model. Both circuits manage to achieve biologically plausible behavior, including sustained spiking and afterhyperpolarization, using a minimal number of components while maintaining the functional dynamics of traditional models.

Discussion

Comparative analysis with existing neuron implementations indicates that the proposed circuits excel in component efficiency, biological plausibility, and ability to exhibit complex dynamics like subthreshold oscillations and sustained spiking. The use of NNDR devices as substitutes for sodium channels in minimal circuits represents a significant advancement in achieving biologically inspired designs with fewer components. This minimalistic approach aids in closing the gap between the electronic implementation and the biological systems they aim to emulate, setting a foundation for more efficient brain-inspired computational systems.

Conclusion

The paper provides a methodology for the design of minimal neuron circuits that leverage biologically inspired models to achieve plausible and efficient spiking behavior. The INa,p+IK model serves as a focal point for these design strategies, allowing for the recreation of complex neuronal dynamics with simplified circuits. The research lays a framework for scalable hardware implementations that mirror the efficiency and parallelism of natural neural networks, contributing to the development of neuromorphic systems. The methodology and circuit designs provided in this paper highlight the potential for future enhancements in spiking neural networks that prioritize biological plausibility and scalability.