Abstract
The recent years are characterized by intensive applications of the methodology and mathematical apparatus of quantum theory, quantum-like modeling, in cognition, psychology, and decision making. In spite of the successful applications of this approach to a variety of psychological effects, e.g., the order, conjunction, disjunction, and response replicability effects, one may (but need not) feel dissatisfaction due to the absence of clear coupling to the neurophysiological processes in the brain. For the moment, this is just a phenomenological approach. In this paper we construct the quantum-like representation of the networks of communicating neurons. It is based not on standard quantum theory, but on generalized probability theory (GPT) with the emphasis of the operational measurement approach. We employ GPT's version which is based on ordered linear state space (instead of complex Hilbert space). A network of communicating neurons is described as a weighted ordered graph that in turn is encoded by its weight matrix. The state space of weight matrices is embedded in GPT with effect-observables and state updates within measurement instruments theory. The latter plays the crucial role. This GPT based model shows the basic quantum-like effects, as e.g. the order, non-repeatability, and disjunction effects; the latter is also known as interference of decisions. This GPT coupling also supports quantum-like modeling in medical diagnostic for neurological diseases, as depression and epilepsy. Although the paper is concentrated on cognition and neuronal networks, the formalism and methodology can be straightforwardly applied to a variety of biological and social networks.
Abstract (translated)
近年来，量子理论的方法和数学工具被广泛应用于认知、心理及决策领域。尽管这种方法在多种心理效应（例如顺序效应、联合效应、析取效应和反应可重复性效应）中有成功的应用，但人们可能（也并非一定如此）会因为缺乏与大脑神经生理过程的明确联系而感到不满。目前，这仅仅是一种现象学方法。在这篇论文中，我们构建了神经元通信网络的量子类似表示。它基于广义概率理论（GPT），而不是标准量子理论，并特别强调操作测量的方法。我们采用的是基于有序线性状态空间（而非复数希尔伯特空间）的GPT版本。一个神经元通信网络被描述为加权有序图，进而通过其权重矩阵进行编码。权重矩阵的状态空间嵌入在GPT中，其中效应-可观测量和状态更新依据于测量仪器理论。后者起着至关重要的作用。这个基于GPT的模型展现了基本的量子类似效应，例如顺序效应、不可重复性和析取效应；后者也被称为决策中的干扰现象。这种GPT耦合还支持对神经性疾病（如抑郁和癫痫）进行医学诊断方面的量子类似建模。尽管论文主要集中在认知和神经网络上，但其形式主义和方法论可以被直接应用于各种生物和社会网络。
URL
https://arxiv.org/abs/2411.00036
