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Analysis of biologically plausible neuron models for regression with spiking neural networks

Mario De Florio, Adar Kahana, George Em Karniadakis

TL;DR

The paper addresses the challenge of using Spiking Neural Networks (SNNs) for regression in Scientific Machine Learning by comparing four biologically plausible membrane models—Leaky Integrate-and-Fire, FitzHugh-Nagumo, Izhikevich, and Hodgkin-Huxley—under two numerical solvers, Euler and Runge–Kutta 4th order. It demonstrates that more expressive membrane models (IZH, HH) yield lower regression error while producing fewer spikes, albeit with higher per-step computation. The study uses a shallow SNN with a single membrane layer and a trainable synapse, optimized by backpropagation on the output layer, and evaluates performance on three functions with varied smoothness, both with and without noise. The findings highlight a trade-off between accuracy and energy usage, suggesting that biologically faithful neurons can improve SciML SNN performance and reduce energy consumption on neuromorphic hardware, guiding model selection for regression tasks.

Abstract

This paper explores the impact of biologically plausible neuron models on the performance of Spiking Neural Networks (SNNs) for regression tasks. While SNNs are widely recognized for classification tasks, their application to Scientific Machine Learning and regression remains underexplored. We focus on the membrane component of SNNs, comparing four neuron models: Leaky Integrate-and-Fire, FitzHugh-Nagumo, Izhikevich, and Hodgkin-Huxley. We investigate their effect on SNN accuracy and efficiency for function regression tasks, by using Euler and Runge-Kutta 4th-order approximation schemes. We show how more biologically plausible neuron models improve the accuracy of SNNs while reducing the number of spikes in the system. The latter represents an energetic gain on actual neuromorphic chips since it directly reflects the amount of energy required for the computations.

Analysis of biologically plausible neuron models for regression with spiking neural networks

TL;DR

The paper addresses the challenge of using Spiking Neural Networks (SNNs) for regression in Scientific Machine Learning by comparing four biologically plausible membrane models—Leaky Integrate-and-Fire, FitzHugh-Nagumo, Izhikevich, and Hodgkin-Huxley—under two numerical solvers, Euler and Runge–Kutta 4th order. It demonstrates that more expressive membrane models (IZH, HH) yield lower regression error while producing fewer spikes, albeit with higher per-step computation. The study uses a shallow SNN with a single membrane layer and a trainable synapse, optimized by backpropagation on the output layer, and evaluates performance on three functions with varied smoothness, both with and without noise. The findings highlight a trade-off between accuracy and energy usage, suggesting that biologically faithful neurons can improve SciML SNN performance and reduce energy consumption on neuromorphic hardware, guiding model selection for regression tasks.

Abstract

This paper explores the impact of biologically plausible neuron models on the performance of Spiking Neural Networks (SNNs) for regression tasks. While SNNs are widely recognized for classification tasks, their application to Scientific Machine Learning and regression remains underexplored. We focus on the membrane component of SNNs, comparing four neuron models: Leaky Integrate-and-Fire, FitzHugh-Nagumo, Izhikevich, and Hodgkin-Huxley. We investigate their effect on SNN accuracy and efficiency for function regression tasks, by using Euler and Runge-Kutta 4th-order approximation schemes. We show how more biologically plausible neuron models improve the accuracy of SNNs while reducing the number of spikes in the system. The latter represents an energetic gain on actual neuromorphic chips since it directly reflects the amount of energy required for the computations.
Paper Structure (10 sections, 14 equations, 3 figures, 1 table)

This paper contains 10 sections, 14 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Biological Neuron Models
  3. Leaky Integrate-and-Fire model
  4. FitzHugh–Nagumo model
  5. Izhikevich model
  6. Hodgkin-Huxley model
  7. Numerical methods
  8. Euler method
  9. Runge-Kutta 4th order method
  10. Results and Discussions

Figures (3)

  • Figure 1: Sketch of an SNN architecture. The spiking data is used as inputs to Hodgkin-Huxley neurons (membranes) and then fed into a synapse. In this architecture, we have a membrane potential that creates output spikes, followed by a synapse, and another membrane that generates output spikes, followed by a second synapse. Finally, a classification or regression mechanism should be applied. In this study, we employ only one membrane followed by a single synapse to perform regression tasks, as elaborated in the results section.
  • Figure 2: Example of the membrane potential over time for given input spikes. The reset mechanism is set to a resting position without refraction. The top plot presents the input spikes over time. The middle plot presents the membrane activity modeled by the Hodgkin-Huxley model. Notice that when the membrane potential reaches the threshold, an output spike is registered, and the membrane resets. The bottom plot presents the registered output spikes over time.
  • Figure 3: Comparison of function regressions using LIF model and Hodgkin-Huxley model with Euler method in the SNN implementation for three different functions, with and without noise.