The code provided is part of a computational model that belongs to the Hierarchical Gaussian Filter (HGF) framework, specifically targeting binary inputs. The HGF is a perceptual model used in computational neuroscience to describe how the brain processes uncertain information. This model focuses on hierarchical Bayesian inference, a process believed to occur in the brain, which allows organisms to make sense of noisy sensory inputs. ### Biological Basis 1. **Hierarchical Processing:** - The HGF model is hierarchically structured, reflecting the layered processing of sensory information in the brain. In biological systems, this hierarchy is seen in the sensory processing pathways where simpler features are processed at lower levels and integrated into more complex representations higher up in the hierarchy. 2. **Bayesian Inference:** - The model implements Bayesian principles, reflecting the idea that the brain uses probabilistic reasoning to interpret sensory information. This is consistent with the notion that neurons in the brain compute and update beliefs about the environment based on incoming sensory data and prior knowledge. 3. **Adaptive Learning:** - HGF incorporates learning rates that adapt based on the estimated uncertainty of the input. This adaptability is biologically analogous to synaptic plasticity, where the strength of connections between neurons is modified based on experience and error feedback. 4. **Uncertainty Representation:** - The model's representation of uncertainty resembles how the brain represents variability and noise in sensory inputs. Uncertainty is modeled through parameters such as µ (mean expectation) and σ² (variance), mirroring the brain's need to optimize responses in uncertain environments. 5. **Predictive Coding:** - The HGF model aligns with the predictive coding theory of brain function. This theory suggests that the brain continuously generates predictions of sensory input and updates them based on discrepancies (prediction errors) between expected and actual inputs, a process that the time-series updates in the code emulate. 6. **Neuromodulatory Influences:** - With parameters like φ (phi) and κ (kappa), the model reflects the influence of neuromodulators (e.g., dopamine and acetylcholine) on learning and inference processes. These parameters impact the volatility and uncertainty estimation, akin to how neurotransmitters modulate attention and learning in the brain. ### Code Connections - **Level (`l`) Structure:** The code determines levels based on parameters, mirroring hierarchical levels of sensory integration in the brain. - **Time Axis (`t` and `ts`):** Represents trial-based learning and adaptation over time, capturing the temporal dynamics of perception similar to trial-based experiments in cognitive neuroscience. - **Input and Responses:** The inputs (`r.u`) and responses (`r.y`) plotted contrast trial inputs to previous state expectations, akin to biological experiments where stimuli and responses are used to study neural processing. In summary, this model serves as a mathematical abstraction of how the brain processes, learns from, and adapts to uncertain sensory information through hierarchical processing and Bayesian inference, offering theoretical insights into neural computation and learning dynamics.