Coupling Quantum-Like Cognitive Models with Neuronal Networks Using Generalized Probability Theory

Core Concepts

This paper proposes a mathematical model using Generalized Probability Theory (GPT) to bridge the gap between quantum-like cognitive models and the neurophysiological processes in neuronal networks, particularly addressing the order, interference, and non-repeatability effects observed in cognitive experiments.

Abstract

Khrennikov, A., Ozawa, M., Benninger, F., & Shor, O. (2024). Coupling quantum-like cognition with the neuronal networks within generalized probability theory. arXiv preprint arXiv:2411.00036.

This paper aims to address the challenge of connecting the successful phenomenological application of quantum-like models in cognitive psychology with the underlying neurophysiological mechanisms in the brain. The authors propose a novel approach using Generalized Probability Theory (GPT) to model the behavior of neuronal networks and demonstrate how this framework can account for key quantum-like effects observed in cognitive experiments.

Key Insights Distilled From

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

by Andrei Khren... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2411.00036.pdf

Deeper Inquiries

How can this GPT-based model be extended to incorporate learning and adaptation in neuronal networks, and how would this contribute to our understanding of cognitive processes like decision-making and memory?

This GPT-based model, centered on weighted directed graphs representing neuronal networks, can be extended to incorporate learning and adaptation by adjusting the weight matrix ω over time. Here's how:

Learning Rules: Implement learning rules inspired by Hebbian learning or backpropagation. These rules would modify the weights (ωij) based on the activity and correlation between connected neurons. For instance, if neurons ni and nj frequently fire together, the weight ωij representing the connection strength from ni to nj would increase, reflecting a strengthened connection.

Synaptic Plasticity: Introduce mechanisms mirroring synaptic plasticity, where the efficacy of signal transmission between neurons changes over time. This could involve:

Long-Term Potentiation (LTP): Persistent strengthening of synapses based on recent patterns of activity.
Long-Term Depression (LTD): Weakening of synaptic connections due to low-frequency stimulation or uncorrelated activity.

Feedback Loops: Incorporate feedback loops within the network architecture. These loops would allow the network to learn from its outputs and adjust its internal representations based on the success or failure of previous actions or decisions.

Contribution to Understanding Cognitive Processes:

Decision-Making: By incorporating learning and adaptation, the model can simulate how neuronal networks learn to make decisions based on past experiences and feedback. Changes in the weight matrix over time would reflect the formation of preferences, biases, and decision strategies.

Memory: The model could provide insights into how memories are encoded and retrieved in neuronal networks. Strengthening of specific connections (weights) could represent the formation of memory traces, while reactivation of these connections could simulate memory recall.

Contextual Adaptation: The model can demonstrate how neuronal networks adapt to changing environments and contexts. The dynamic adjustment of weights would allow the network to learn new associations and modify its behavior based on new information.
By incorporating learning and adaptation, this GPT-based model can evolve from a static representation of neuronal networks to a dynamic framework capable of simulating complex cognitive processes. This will provide a more realistic and insightful tool for understanding the neural basis of cognition.

Could the success of quantum-like models in cognitive psychology be attributed to emergent properties of complex neuronal networks rather than implying genuine quantum processes in the brain?

Yes, the success of quantum-like models in cognitive psychology could indeed be attributed to emergent properties of complex neuronal networks rather than necessitating genuine quantum processes in the brain.
Here's why:

Complexity Mimicking Quantum Behavior: Neuronal networks, with their billions of interconnected neurons exhibiting nonlinear dynamics and feedback loops, can give rise to emergent properties that statistically resemble quantum phenomena. These properties, such as superposition-like states, entanglement-like correlations, and interference effects, might arise from the complex interactions within the network, without requiring neurons to operate under quantum mechanical principles.

Generalized Probability Theory as a Bridge: The GPT framework, as described in the context, provides a mathematical framework that can accommodate both classical and quantum probabilities. This suggests that the observed quantum-like behavior in cognitive experiments might be better explained by a generalized probability theory that captures the inherent uncertainty and contextuality of cognitive processes, rather than by invoking genuine quantum processes.

Quantum-like as a Metaphor: It's crucial to remember that the use of "quantum" in cognitive models is often metaphorical. It's a way to leverage the mathematical formalism of quantum theory to describe the non-classical, contextual, and probabilistic nature of human cognition, without implying that the brain is a quantum computer.
In essence, the success of quantum-like models might point towards the brain operating as a complex system capable of exhibiting emergent properties that share statistical similarities with quantum systems, rather than requiring neurons themselves to behave as quantum objects.
Further research is needed to disentangle whether these quantum-like features are merely convenient mathematical descriptions or whether they hint at deeper, yet-to-be-discovered principles governing information processing in the brain.

If consciousness arises from the intricate interactions within and between neuronal networks, could this GPT framework provide insights into the nature of subjective experience and its relationship to the physical world?

While it's a significant leap to claim that this GPT framework can fully unravel the enigma of consciousness, it could potentially offer some valuable insights into the neural correlates of subjective experience and its connection to the physical world. Here's how:

Integrated Information and Subjective States: The GPT model, by representing neuronal networks as weighted graphs, could be used to explore how the structure and dynamics of these networks relate to different conscious states. For instance, changes in the weight matrix, reflecting altered connectivity patterns, might correspond to shifts in perception, attention, or emotional states.

Emergence from Information Processing: The framework's emphasis on information processing within neuronal networks aligns with the view that consciousness arises from the way information is integrated and processed in the brain. By studying the flow and transformation of information within the GPT model, we might gain insights into how subjective experience emerges from the physical interactions of neurons.

Contextuality and the Subjective Perspective: GPT, by its very nature, incorporates contextuality, meaning that the outcome of a measurement (or a cognitive process) depends on the context in which it's embedded. This aligns well with the subjective nature of experience, where our perception and interpretation of the world are shaped by our past experiences, current state, and the specific context of a situation.

Bridging the Explanatory Gap: While GPT alone might not bridge the explanatory gap between the physical and subjective, it could provide a mathematical language that connects neural activity to measurable behavioral or cognitive outcomes. By correlating specific patterns of network activity within the GPT model to reported subjective experiences, we might begin to map the neural footprints of consciousness.

However, it's crucial to acknowledge the limitations:

Subjectivity is Immeasurable: The inherently subjective nature of experience poses a significant challenge. We can't directly measure or observe someone else's subjective feelings or qualia.

GPT is a Model: It's essential to remember that the GPT framework is a mathematical model, an abstraction of reality. While it can provide valuable insights, it's not a one-to-one representation of the brain or consciousness.
In conclusion, while this GPT framework might not provide a definitive answer to the hard problem of consciousness, it offers a promising avenue for exploring the neural basis of subjective experience. By investigating how information processing within interconnected neuronal networks gives rise to complex, context-dependent behavior, we might inch closer to understanding the intricate relationship between the physical world and our subjective experience of it.