The code provided represents a computational model rooted in the framework of the Hierarchical Gaussian Filter (HGF). The HGF is a model employed to understand how the brain processes uncertain sensory inputs to form beliefs about the world. Here's a breakdown of its biological basis: ### Biological Principles 1. **Hierarchical Model of Perception**: - **Levels of Representation**: The HGF assumes that perception is hierarchical. Each level represents a belief or state (e.g., sensory input, latent causes of sensory input, etc.), with higher levels representing beliefs about more abstracted or hidden states. - **Biological Analog**: This hierarchical processing mimics brain structures like the cortical hierarchy where primary sensory areas process raw sensory data, and higher cortical areas integrate this into more abstract representations. 2. **Bayesian Inference**: - **Predictive Coding**: The brain is modeled as performing Bayesian inference, where prior beliefs are updated in light of new sensory evidence. - **Prediction Errors**: Prediction errors (discrepancies between expected and observed inputs) are used to update beliefs. This is reminiscent of the brain's drive to minimize prediction errors, a concept central to predictive coding theories of perception and cognition. 3. **Volatility and Learning Rates**: - **Learning Rates (µ and π)**: These parameters represent the flexibility of updating beliefs based on new information, akin to synaptic plasticity in neural circuits. - **Volatility (δ)**: The model captures how perceived environmental volatility affects learning rates. More volatile environments are thought to increase the brain’s sensitivity to prediction errors, adjusting the weight of new evidence in updating beliefs. 4. **Gaussian Assumptions**: - **Gaussian Filters**: The model assumptions imply that beliefs and their uncertainties are normally distributed. This reflects the idea that neural responses often follow a Gaussian-like distribution due to the aggregate effect of many synaptic inputs. 5. **Precision Modulation**: - **Precision (Inverse of Variance)**: It represents confidence in beliefs, with higher precision indicating more confidence. This concept aligns with the idea that the brain allocates resources differentially to different sensory signals based on their precision or reliability. 6. **Dynamic Updating**: - **Trial-Wise Updates**: The model captures the dynamic nature of belief updating over time. Neurons exhibit temporally-dependent synaptic plasticity, reflecting ongoing adjustments to inputs and environmental changes. ### Summary Overall, the HGF model encapsulated in the code reflects biological processes involved in Bayesian inference, predictive coding, and hierarchical processing. It encapsulates how the brain dynamically integrates sensory information with prior beliefs to form coherent perceptions, adjusting these beliefs based on environmental context and perceived uncertainty. This approach provides a computationally tractable framework to investigate how the brain achieves the remarkable feat of dynamic sensory integration and decision-making under uncertainty.