Phenomenological Model of Superconducting Optoelectronic Loop Neurons

TL;DR

This paper introduces a phenomenological modeling framework for superconducting optoelectronic loop neurons, significantly improving computational efficiency while accurately capturing their behavior, facilitating large-scale network simulations and interdisciplinary connections.

Contribution

A new phenomenological model for superconducting optoelectronic loop neurons that reduces computational complexity and links to broader scientific fields.

Findings

Model reduces simulation time by a factor of ten thousand.

Maintains accuracy of one part in ten thousand compared to circuit simulations.

Enables large-scale network simulations of superconducting optoelectronic neurons.

Abstract

Superconducting optoelectronic loop neurons are a class of circuits potentially conducive to networks for large-scale artificial cognition. These circuits employ superconducting components including single-photon detectors, Josephson junctions, and transformers to achieve neuromorphic functions. To date, all simulations of loop neurons have used first-principles circuit analysis to model the behavior of synapses, dendrites, and neurons. These circuit models are computationally inefficient and leave opaque the relationship between loop neurons and other complex systems. Here we introduce a modeling framework that captures the behavior of the relevant synaptic, dendritic, and neuronal circuits at a phenomenological level without resorting to full circuit equations. Within this compact model, each dendrite is discovered to obey a single nonlinear leaky-integrator ordinary differential equation, while a neuron is modeled as a dendrite with a thresholding element and an additional feedback mechanism for establishing a refractory period. A synapse is modeled as a single-photon detector coupled to a dendrite, where the response of the single-photon detector follows a closed-form expression. We quantify the accuracy of the phenomenological model relative to circuit simulations and find that the approach reduces computational time by a factor of ten thousand while maintaining accuracy of one part in ten thousand. We demonstrate the use of the model with several basic examples. The net increase in computational efficiency enables future simulation of large networks, while the formulation provides a connection to a large body of work in applied mathematics, computational neuroscience, and physical systems such as spin glasses.