# Transmission Neural Networks: Inhibitory and Excitatory Connections

arXiv: https://arxiv.org/abs/2604.04246 · HTML: https://mlsanity.com/paper/2604.04246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Transmission Neural Networks: From Virus Spread Models to Neural Networks](https://mlsanity.com/paper/2208.03616/) (2022)
- [Transmission Neural Networks: Approximate Receding Horizon Control for Virus Spread on Networks](https://mlsanity.com/paper/2510.22871/) (2025)

## Abstract (arXiv)

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.