In this article, we explore the concept of field theories and their application to the study of neural activity. We begin by defining what field theories are and how they differ from traditional dynamic models. A field theory is a mathematical framework that represents the collective behavior of a large number of agents, such as neurons in the brain, by modeling them as a set of interacting fields.
Unlike traditional dynamic models, which represent each agent individually, field theories aggregate the degrees of freedom of many agents into a single field. This allows for a more compact and efficient representation of complex neural systems. However, this simplification also means that field theories can’t capture every detail of individual agent behavior.
We then compare our field theory approach to other statistical field theories, such as Mean Field Theory, which simplify the model by neglecting interaction delays or variations in connectivity between agents. Our approach maintains a more detailed account of individual dynamics and connectivities while still retaining key features and objectives of neural field dynamics.
We also discuss how our field theory translates microscopic models into larger collective scales, allowing us to compute probabilities of different outcomes for each collective state of the system. This approach provides a unique advantage over traditional dynamic models as it allows for a more detailed account of individual agent behavior while still retaining key features and objectives of neural field dynamics.
In summary, field theories provide a powerful tool for modeling complex systems by representing them as interacting fields rather than individual agents. By aggregating the degrees of freedom of many agents into a single field, field theories enable more efficient and compact representations of complex systems, while still capturing key features and objectives of neural field dynamics.
Field Modeling: A Probabilistic Approach to Compute Global Outcomes
