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arXiv · 2406.06726

The Price of Cognition and Replicator Equations in Parallel Neural Networks

Armen Bagdasaryan·Antonios Kalampakas·Mansoor Saburov
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Abstract

In this paper, we are aiming to propose a novel mathematical model that studies the dynamics of synaptic damage in terms of concentrations of toxic neuropeptides/neurotransmitters during neurotransmission processes. Our primary objective is to employ Wardrop's first and second principles within a neural network of the brain. In order to comprehensively incorporate Wardrop's first and second principles into the neural network of the brain, we introduce two novel concepts: \textit{neuropeptide's (neurotransmitter's) equilibrium} and \textit{synapses optimum}. The \textit{neuropeptide/neurotransmitter equilibrium} refers to \textit{a distribution of toxic neuropeptides/neurotransmitters that leads to uniform damage across all synaptic links}. Meanwhile, \textit{synapses optimum} is \textit{the most desirable distribution of toxic neuropeptides/neurotransmitters that minimizes the cumulative damage experienced by all synapses}. In the context of a neural network within the brain, an analogue of the price of anarchy is \textit{the price of cognition} which is \textit{the most unfavorable ratio between the overall impairment caused by toxic neuropeptide's (neurotransmitter's) equilibrium in comparison to the optimal state of synapses (synapses optimum)}. To put it differently, \textit{the price of cognition} measures \textit{the loss of cognitive ability resulting from increased concentrations of toxic neuropeptides/neurotransmitters}. Additionally, a replicator equation is proposed within this framework that leads to the establishment of the synapses optimum during the neurotransmission process.

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Armen Bagdasaryan, Antonios Kalampakas, Mansoor Saburov. 2024-06-10. The Price of Cognition and Replicator Equations in Parallel Neural Networks. https://arxiv.org/abs/2406.06726

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