## Biological Basis of the Model The provided code is designed to configure a computational model known as the Hierarchical Gaussian Filter (HGF), which is a sophisticated tool used in computational neuroscience to model learning and decision-making processes. This particular configuration is tailored for modeling decision-making in a multi-armed bandit task, which is a type of problem that deals with making choices under uncertainty to maximize rewards. ### Biological Relevance #### 1. **Learning and Decision-Making** The HGF is grounded in the Bayesian brain hypothesis, which suggests that the brain interprets sensory information and makes decisions through Bayesian inference. In this context, the HGF aims to model how humans learn and make decisions based on uncertain information, akin to how synaptic weights in neural networks are adjusted in response to incoming signals and environmental feedback. - **Multi-Armed Bandit Task**: This task emulates situations where individuals choose between different options (or "bandits") to receive rewards, which is analogous to how animals (including humans) explore and exploit different strategies to maximize their survival chances and reproductive success. #### 2. **Hierarchical Processing** The model uses a hierarchical structure, reflecting the hierarchical organization in the brain, where different levels of processing occur, from initial sensory input to complex interpretative functions leading to decision-making. - **Levels of Processing**: In the code, `n_levels` denotes these hierarchical levels, analogous to how sensory inputs might be processed at lower levels (like the thalamus) and integrated at higher levels (like the cortex). #### 3. **Prediction and Error Processing** The model implements concepts like prediction errors, which play a crucial role in learning and updating beliefs about the environment in the brain. Different forms of prediction errors (`da`, `dau`, `ud`) are represented in the model: - **Prediction Errors**: In biological systems, dopamine neurons are known to encode reward prediction errors, serving as a signal for the brain to update beliefs or expectations about rewards. #### 4. **Volatility and Uncertainty Management** The incorporation of volatility prediction errors and uncertainty (`sa`, `sahat`) is critical to understanding how the brain manages uncertainty, which is essential in dynamic and unpredictable environments. - **Volatility**: Certain brain regions, such as the prefrontal cortex and the amygdala, are believed to be involved in estimating environmental volatility and adapting decision-making strategies accordingly. ### Key Parameters and Their Biological Interpretation - **`mu` and `sigma` (or `sa`)**: These parameters represent beliefs about the environment (means and variances), akin to neuronal estimates of expected rewards and uncertainties. - **`phi` and `kappa`**: These parameters handle the transformation and scaling of beliefs between hierarchical levels, similar to synaptic gain and re-weighting that occur in neural processing as information ascends the cortical hierarchy. - **`omega` and `alpha`**: They capture dynamic adjustments in belief updating, potentially reflecting neuromodulatory influences such as those exerted by neurotransmitters like dopamine, which modulate learning rates based on reward prediction error signals. Overall, the model attempts to capture the probabilistic and hierarchical nature of how the brain processes information, learns from the environment, and guides actions under uncertainty, drawing on both neuronal principles and computational theories of learning and inference.