Functional connectome-based Hopfield Networks: attractor dynamics, cognitive correlates, and clinical insights into Empirical Attractor Networks

Understanding the dynamics of brain function remains a core challenge in neuroscience, with neuroimaging, particularly functional magnetic resonance imaging (fMRI), playing a crucial role in studying brain structure and function. Research efforts that analyze recurring neurological patterns, so called brain states, aim to elucidate the underlying structures that shape neural activations. We introduce the functional connectome-based Hopfield network (fcHNN) as a phenomenological model for macro-scale brain dynamics and employ it across five different datasets, covering resting state, task-based and clinical fMRI data. The fcHNN is not trained or optimized to mimic characteristics of neural activity, but is rather initialized empirically with functional connectivity values, which allows the network to uncover neurobiologically valid attractor states - energy-minimal activity patterns - from within its memory. To strengthen the neurobiological validity of the attractor states, we present results that highlight the associations towards behavior and cognition, by the means of dynamic analysis and predictive modeling. In addition to these descriptive analyses, we also explore the fcHNN’s ability to capture and reconstruct key aspects of brain activity in clinical and task data. In summary, the functional connectome-based Hopfield network serves as a lightweight, nearly parameter-free model that effectively extracts and visualizes brain state dynamics, and offers both descriptive and generative capabilities, potentially aiding in the understanding and treatment of neurological and psychiatric disorders.