## Biological Basis of the Code The provided code models decision-making processes in a multi-armed bandit task using the Hierarchical Gaussian Filter (HGF). This model simulates how an agent (such as a human or an animal) learns and makes decisions when faced with uncertain and dynamically changing environments, reflecting some fundamental principles of cognitive and neural function observed in biological systems. ### Core Biological Concepts 1. **Bayesian Inference:** - The HGF model embodies the concept of Bayesian inference, which is pivotal in understanding how the brain processes uncertain information. The brain integrates prior beliefs with new evidence to update its beliefs, optimizing behavior under uncertainty—a cornerstone of cognitive neuroscience. 2. **Levels of Processing:** - The model represents hierarchical levels of processing akin to the layered structure of the brain. Each level consists of parameters like `mu` (mean or belief at each level), `pi` (precision or inverse uncertainty), and `ka` (volatility). The layers may parallel neural circuits that process ascending complexity of information, from stimuli perception to higher-order decision-making. 3. **Volatility and Uncertainty:** - Biological brains must adaptively account for uncertainty and change (volatility) in the environment. In the code, parameters such as `rho`, `ka`, and `om` adjust the uncertainty and volatility, reflecting adjustments in neuronal activity that accommodate learning about the environment. 4. **Prediction Errors and Learning:** - The model computes prediction errors (`da`) at each level, analogous to dopaminergic prediction errors observed in the brain. Prediction errors are crucial for learning; they signal the mismatch between expected and received outcomes, driving updates to cognitive representations—a process supported by neural circuits, particularly within the dopaminergic and prefrontal regions. 5. **Coupled Updating:** - For settings with two bandits (`coupled` is enabled), the model uses a constraint that resembles competitive interaction or normalization processes seen in neural populations, where changes in belief about one option influence the other. This is reflected in the biological decision-making circuits that balance competing choices. 6. **Sequential Decision Making:** - The HGF supports modeling how decisions evolve over trials, where past experiences influence future behavior, similar to how the brain accumulates information over time to refine its predictions and actions. 7. **Precision-Weighted Learning Rates (`psi`, `epsi`):** - These concepts relate to the adaptive adjustment of learning rates based on the precision of beliefs, echoing the idea that the brain optimizes the impact of new information proportional to its reliability, a principle seen in both animal learning and human cognitive flexibility. ### Conclusion The HGF model as implemented in this code simulates how an agent learns from interactions with its environment by updating beliefs in a Bayesian manner, emphasizing hierarchical processing, prediction error signaling, and adaptive learning rates. These computational concepts mirror fundamental biological principles found in neural substrates of learning and decision-making, highlighting the brain's capacity to adapt under uncertainty and volatility, crucial for survival in dynamic environments.