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Discrete Event System Modeling of Neuromorphic Circuits

Koen Scheres, Rodolphe Sepulchre

TL;DR

The paper tackles the problem of extracting discrete-event (DES) models from continuous-time biophysical neuromorphic circuits to enable formal analysis and design of neuromorphic control systems. It develops a systematic mapping from excitable neuron dynamics and synaptic interactions to untimed DES automata, distinguishing internal versus external transitions and excitatory versus inhibitory inputs. The authors demonstrate DES representations for single neurons, synaptic motifs, and small networks (including WTA structures) and outline a practical realization method that builds neuromorphic circuits from DES building blocks. They argue that DES complement Conductance-based models by clarifying event ordering and enabling verification and design of decision-making circuitry with potential robotics applications.

Abstract

Excitable neuromorphic circuits are physical models of event behaviors: their continuous-time trajectories consist of sequences of discrete events. This paper explores the possibility of extracting a discrete-event model out of the physical continuous-time model. We discuss the potential of this methodology for analysis and design of neuromorphic control systems.

Discrete Event System Modeling of Neuromorphic Circuits

TL;DR

The paper tackles the problem of extracting discrete-event (DES) models from continuous-time biophysical neuromorphic circuits to enable formal analysis and design of neuromorphic control systems. It develops a systematic mapping from excitable neuron dynamics and synaptic interactions to untimed DES automata, distinguishing internal versus external transitions and excitatory versus inhibitory inputs. The authors demonstrate DES representations for single neurons, synaptic motifs, and small networks (including WTA structures) and outline a practical realization method that builds neuromorphic circuits from DES building blocks. They argue that DES complement Conductance-based models by clarifying event ordering and enabling verification and design of decision-making circuitry with potential robotics applications.

Abstract

Excitable neuromorphic circuits are physical models of event behaviors: their continuous-time trajectories consist of sequences of discrete events. This paper explores the possibility of extracting a discrete-event model out of the physical continuous-time model. We discuss the potential of this methodology for analysis and design of neuromorphic control systems.

Paper Structure

This paper contains 19 sections, 1 theorem, 1 equation, 11 figures.

Table of Contents

  1. Introduction
  2. Discrete Event Systems
  3. Neuromorphic Circuits
  4. The event behavior of an excitable neuron
  5. Excitatory and inhibitory synaptic currents
  6. Event triggering by external inputs
  7. Separating the discrete from the continuous
  8. Discrete Event System models of Neuromorphic Circuits
  9. DES models of single neurons
  10. DES models of synaptic interconnections
  11. Excitatory synapse
  12. Inhibitory synapse
  13. Bursting neurons
  14. DES of a network of neurons
  15. Decision-making in Neuromorphic Circuits
  16. ...and 4 more sections

Key Result

Proposition 1

The discrete dynamics of a winner-take-all network of $N$ post-inhibitory rebound spiking neurons with no excitatory synapses can be captured in an $N+1$ automaton with all-to-all transitions excluding self-loops.

Figures (11)

  • Figure 1: By separating the control stack into a hierarchical structure, it is possible to do fast (real-time) tracking as well as slow decision-making. Adapted from Matni_Ames_Doyle_2024.
  • Figure 2: A neuron is an excitable system: a minor variation in the input can cause a major variation in the output due to the presence of a bifurcation.
  • Figure 3: Circuit representation of Hodgkin-Huxley model.
  • Figure 4: Different responses to stimuli: excitatory spiking and post-inhibitory bursting of the Hodgkin-Huxley model with additional $T$-type $\mathrm{{Ca}^{2+}}$ and slow $\mathrm{K}^+$ ion channels.
  • Figure 5: Automaton representations of single spiking neurons.
  • ...and 6 more figures

Theorems & Definitions (5)

  • Definition 1: Cassandras_Lafortune_2021
  • Definition 2: Cassandras_Lafortune_2021
  • Definition 3
  • Definition 4
  • Proposition 1