Transmission Neural Networks: Inhibitory and Excitatory Connections

2026-04-05

AI Summary

This study addresses the challenge of effectively modeling the influence of inhibitory and excitatory connections on neuronal spiking dynamics within the framework of transmission neural networks. To this end, it introduces—in the first such incorporation—both inhibitory synapses and populations of neurotransmitters into this paradigm, yielding a stochastic network model that features binary neuronal states coupled with dynamic transmission mechanisms. The authors derive an analytical expression for neuronal firing probability and demonstrate through theoretical analysis that the model is equivalent to a two-dimensional continuous-state system. In the limit as the number of neurotransmitters tends to infinity, they formulate a limiting model and establish sufficient conditions for its stability and contractivity. This work thus provides novel modeling and analytical tools for understanding the role of inhibition in spiking neural networks.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper extends the Transmission Neural Network model proposed by Gao and Caines in [1]-[3] to incorporate inhibitory connections and neurotransmitter populations. The extended network model contains binary neuronal states, transmission dynamics, and inhibitory and excitatory connections. Under technical assumptions, we establish the characterization of the firing probabilities of neurons, and show that such a characterization considering inhibitions can be equivalently represented by a neural network where each neuron has a continuous state of dimension 2. Moreover, we incorporated neurotransmitter populations into the modeling and establish the limit network model when the number of neurotransmitters at all synaptic connections go to infinity. Finally, sufficient conditions for stability and contraction properties of the limit network model are established.

Problem

• Transmission Neural Networks
• Inhibitory Connections
• Excitatory Connections
• Neurotransmitter Populations
• Firing Probabilities

Innovation

• Transmission Neural Networks
• Inhibitory Connections
• Neurotransmitter Populations
• Firing Probability Characterization
• Network Stability