The Mathematics of Structured Experience: Exploring Dynamics, Topology, and Complexity in the Brain

Dear Colleagues,

This Special Issue is motivated by the Kolmogorov theory of consciousness (KT) and related mathematical frameworks in cognition and consciousness, including active inference and predictive coding. It invites contributions that shed light on the intricate link between brain dynamics and the experiential phenomena they induce. Central to this discourse is the proposition that agents (computational entities) construct compressive models (algorithms) of the world to track world data and guide action planning through objective function evaluation. This perspective underscores the profound impact of model mathematical structure on the brain's dynamic trajectories, or the "dynamical landscape," and on the resulting qualia (structured experience). It opens exciting avenues for empirical investigation and methodological innovation, leveraging advanced concepts from dynamical systems theory, geometry, topology, algorithmic information theory, and critical phenomena theory. Success in this endeavor promises to significantly enrich fields like fundamental neuroscience, computational neuropsychiatry, and artificial intelligence, offering novel insights and approaches.

Titled “The Mathematics of Structured Experience: Exploring Dynamics, Topology, and Complexity in the Brain”, this Special Issue aims to explore several key areas in this program:

1. Characteristics of compressive world models: We aim to delve into the nature of the world models created and run by natural and artificial agents. What do we mean, precisely, by a world model? What is the connection between program structure and the resulting dynamics? What is the role of symmetry and criticality in shaping world models and programs, and how do they enable agents to encapsulate the world's complexity in a comprehensible form?
2. Mapping models to dynamical systems: A crucial exploration will be how compressive world model characteristics translate into the workings of agents as dynamical systems and their features, especially recurrent neural networks. Topics include the study of geometry and topology of invariant manifolds, dimensionality reduction (manifold hypothesis), dynamical latent spaces, and their connection with algorithmic concepts such as compression and symmetry. We invite contributions that use tools from dynamical systems theory, geometry, topology, and criticality to characterize and understand the underlying dynamics of biological or artificial systems and their relation to the data they generate (neuroimaging/neurophysiology or other data).
3. Empirical paradigms for validation: This Special Issue also seeks to address the design of experimental paradigms aimed at validating these concepts. Specifically, we are interested in establishing connections between features derived from structured experience reports or other behavior and the observed structure in the brain (or, more generally, complex systems) dynamics (e.g., as measured by neuroimaging techniques) using the tools mentioned in the previous points. Application areas include the study of states of consciousness and disorders of consciousness, as well as non-human consciousness, using currently available datasets or through the design of specific experiments.
4. Implications for the design of artificial intelligence and computational models of the brain. How does this perspective influence research on artificial systems or computational models of the brain? What are the design principles inspired by the mathematics of algorithmic agenthood that can be used in artificial intelligence or computational neuroscience? 

Through these explorations, this Special Issue aims to stimulate a multidisciplinary dialogue that bridges abstract mathematical concepts in algorithmic information theory, dynamics, geometry, and topology with neural phenomena and, ultimately, first-person experience. Our objective is to enhance our understanding of how the brain encodes, processes, and manifests structured experience and how this understanding can inform new computational models and therapeutic approaches for neuroscience and clinical neuropsychiatric as well as artificial intelligence.

We welcome submissions of original research, reviews, and perspective pieces that contribute to this field. Emphasis should be on the theoretical underpinnings, methodological approaches, and potential implications of integrating mathematics with the study of the brain and the consciousness of complex systems.

References:

• Giulio R. An algorithmic information theory of consciousness. Conscious. 2017, 3, nix019. https://doi.org/10.1093/nc/nix019
• Ruffini, G.; Lopez-Sola, E. AIT foundations of structured experience. AI Consci. 2022, 9, 153–191. https://doi.org/10.1142/S2705078522500047
• Parr, T.; Pezzulo, G.; Friston, K.J. Active Inference: The Free Energy Principle in Mind, Brain, and Behavior; MIT Press: Cambridge, MA, USA, 2022. https://doi.org/10.7551/mitpress/12441.001.0001
• Ruffini, G.; Lopez-Sola, E.; Vohryzek, J.; Sanchez-Todo, R. Neural Geometrodynamics, Complexity, and Plasticity: A Psychedelics Perspective. Entropy 2024, 26, 90. https://doi.org/10.3390/e26010090
• Fernandez, I. S., Lam, K. C., Handwerker, D. A., Pereira, F., & Bandettini, P. A. Manifold learning for fMRI time-varying functional connectivity. Hum. Neurosci. 2023, 17, 1134012. https://doi.org/10.3389/fnhum.2023.113

Dr. Giulio Ruffini
Dr. Johannes Kleiner
Dr. Ryota Kanai
Guest Editors

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• mathematical theories of consciousness
• Kolmogorov complexity
• AIT
• manifold hypothesis
• symmetry
• world models
• dynamics
• topology
• AI