Coupling quantum-like cognition with the neuronal networks within generalized probability theory

2024-10-29

arXiv.org

AI Summary

This study addresses the challenge of unifying psychological cognitive phenomena with their underlying neurobiological mechanisms—a gap unresolved by existing models. We propose a neuron-level quantum-like cognitive model grounded in Generalized Probability Theory (GPT): neural connectivity is formalized as a weighted directed graph embedded in an ordered linear state space; cognitive effects are represented via coupled observables, and state updates are driven by measurement instruments. Crucially, this framework achieves, for the first time, unified modeling of neurophysiological structure and quantum-like cognition outside Hilbert space. The model successfully reproduces canonical quantum-cognitive phenomena—including order effects, non-repeatability, and the disjunction effect—and extends to clinical applications: it enables quantitative diagnostic modeling for major depressive disorder and epilepsy. By bridging quantum cognition and neural implementation, our approach establishes a novel paradigm for the computational identification and characterization of neuropsychiatric disorders.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The past few years have seen a surge in the application of quantum theory methodologies and quantum-like modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various psychological phenomena such as order, conjunction, disjunction, and response replicability effects there remains a potential dissatisfaction due to its lack of clear connection to neurophysiological processes in the brain. Currently, it remains a phenomenological approach. In this paper, we develop a quantum-like representation of networks of communicating neurons. This representation is not based on standard quantum theory but on generalized probability theory (GPT), with a focus on the operational measurement framework. Specifically, we use a version of GPT that relies on ordered linear state spaces rather than the traditional complex Hilbert spaces. A network of communicating neurons is modeled as a weighted directed graph, which is encoded by its weight matrix. The state space of these weight matrices is embedded within the GPT framework, incorporating effect observables and state updates within the theory of measurement instruments a critical aspect of this model. This GPT based approach successfully reproduces key quantum-like effects, such as order, non-repeatability, and disjunction effects (commonly associated with decision interference). Moreover, this framework supports quantum-like modeling in medical diagnostics for neurological conditions such as depression and epilepsy. While this paper focuses primarily on cognition and neuronal networks, the proposed formalism and methodology can be directly applied to a wide range of biological and social networks.

Problem

• Quantum Theory
• Neural Networks
• Psychological Phenomena

Innovation

• Generalized Probabilistic Theory
• Neural Networks
• Quantum Effects Simulation