The provided MATLAB code is a part of a computational neuroscience toolbox that models perception and decision-making processes using a mathematical framework called the Hierarchical Gaussian Filter (HGF). This specific function `tapas_rw_binary_dual_plotTraj` is used to visualize the trajectories of perceptual and decision variables in a reinforcement learning framework, specifically for multi-armed bandit tasks. ### Biological Basis of the Code #### Reinforcement Learning and Multi-Armed Bandit Tasks 1. **Decision-Making Model**: The code models biological decision-making processes in multi-armed bandit tasks. These tasks require choosing between multiple options (bandits) with uncertain rewards, mimicking real-life decision-making where organisms must choose between foraging locations or actions based on varying reward probabilities. 2. **Probabilistic Environment**: The model assumes a probabilistic environment where the rewards depend on the hidden states of the environment. This reflects how biological organisms must infer environmental states based on incomplete and noisy sensory information. #### Hierarchical Gaussian Filter (HGF) 1. **Perception and Expectancy**: The representation of `r.p_prc.v_0` and `r.traj.v` corresponds to the prior and posterior estimates of the reward expectation, akin to how the brain generates and updates expectations based on prior knowledge and incoming sensory evidence. 2. **Learning and Adaptation**: The model's parameter `\alpha`, shown in the title of plotted results, likely corresponds to a learning rate, representing synaptic or neuroplastic changes where the strength of the connection between neurons adapts based on experience. #### Biological Neural Processes 1. **Neural Prediction Error**: The concept of a prediction error, a difference between expected and received reward, is central to many neural learning theories. This model likely calculates such errors to update expectations, paralleling dopaminergic signaling pathways in the brain. 2. **Trial-Based Learning**: With the focus on trial numbers (`n` and `ts`) and the updating of expectations across trials, this reflects the iterative learning processes observed in both animal and human studies of behavior under uncertainty. #### Visualization and Model Outputs 1. **Behavioral Responses and Irregularities**: The code includes the potential to plot responses `r.y`, and identifies irregular responses which reflect real-world irregularities in biological response patterns due to noise or suboptimal decision strategies. The code thus embodies a sophisticated computational model of learning and decision-making grounded in biological processes. It aims to simulate how cognitive systems interpret ambiguous environments, form expectations, and adjust behavior, echoing key neural mechanisms that enable adaptive behavior in complex, dynamic settings.