The code provided is a part of the Hierarchical Gaussian Filter (HGF) model, which is a computational model used in neuroscience to simulate how individuals perceive and react to dynamic environments. This model is particularly concerned with the way the brain updates beliefs and expectations in response to sensory input, capturing crucial aspects of cognitive and perceptual belief updating via a hierarchical Bayesian framework.
The code models hierarchical Bayesian belief updating, which parallels the cognitive processes that occur in the brain. In the biological system, the brain is thought to use a hierarchical structure for processing information, where higher cognitive layers regulate and predict the flow of information at lower sensory layers. This reflects the multi-level Bayesian inference the code performs, with different levels (l in the code) potentially representing different cognitive or sensory layers.
A fundamental mechanism in the brain is the generation of predictions about incoming sensory data, followed by the updating of beliefs based on prediction errors. The code captures this via the mu (mean) and pi (precision) parameters, which represent the agent's beliefs and the associated confidence, respectively. Prediction errors (dau and da) are computed as the difference between expected and actual observations, akin to how the brain might update its beliefs when its predictions do not match incoming sensory input.
The HGF model captures how the brain adapts to changes in environmental uncertainty or volatility, modeled here by parameters like phi, ka, and om, which influence the weighting and influence of prediction errors at different levels. In biology, this reflects how cognitive flexibility and learning rates might adjust depending on the stability or volatility of the environment.
The concept of precision weighting, which is essential in the code (pihat, pi), is related to the degree of reliability or confidence the brain assigns to different sources of information. In neurobiological terms, this might relate to neurophysiological processes where attention is modulated based on the expected precision of sensory input, influencing how sensory signals are prioritized and processed.
While the code does not directly model specific neural mechanisms, the computational principles implemented — hierarchical structure, prediction updates, precision modulation — are consistent with theories about the brain's functioning, such as predictive coding or active inference. These theories posit that neural circuits in the brain (e.g., in the cortical hierarchy) continuously generate predictions and errors to optimize perception and action.
By reflecting these cognitive and neural processes, the HGF model implemented in this code provides insights into how beliefs and expectations might be dynamically regulated in the brain, serving as a bridge between computational theory and biological reality.