# Biological Basis of the Computational Model The code provided represents a computational implementation of the Hierarchical Gaussian Filter (HGF) model for binary inputs in the presence of perceptual uncertainty. This model is rooted in Bayesian principles and aims to simulate learning and adaptation processes observed in the human brain, particularly under conditions of uncertainty. Below are the key biological concepts modeled by the HGF: ## 1. **Cognitive Learning and Adaptation** The HGF model is designed to capture how individuals learn from binary outcomes (e.g., success/failure, reward/no-reward) in uncertain environments. This aligns well with how the human brain adapts and updates beliefs based on new information, reflecting core processes of cognitive adaptation and learning. ## 2. **Hierarchical Structures** The model employs a hierarchical structure to represent different levels of cognitive processing. Each level corresponds to a different timescale or depth of belief updating, akin to hierarchical processing in the brain where higher cognitive functions integrate more abstract and complex information. - **Mu (μ) and Sigma (σ):** These parameters represent expectations (μ) and uncertainties (variances, σ) at different levels of the hierarchy. They are analogous to the probabilistic beliefs and confidence the brain maintains about the environment. ## 3. **Perceptual Uncertainty** The model accommodates perceptual uncertainty, which is a critical aspect of how humans interact with their environment. This reflects the variability and noise inherent in sensory information processing, where sensory inputs may be ambiguous, requiring the system to estimate and manage uncertainties. ## 4. **Drift and Volatility** - **Rho (ρ):** This parameter signifies the drift rate, representing how beliefs gradually evolve over time without external input. It is related to the brain's ability to maintain and update existing knowledge over time. - **Omega (ω):** Represents environmental volatility, allowing the model to account for rapidly changing environments. This is analogous to how the brain must assess the stability of contextual information and cues. ## 5. **Predictive Coding and Error Correction** Predictive coding models suggest that the brain continuously generates predictions about incoming sensory data and updates these predictions based on the discrepancies (prediction errors). The HGF model incorporates this by estimating and updating beliefs based on prediction errors, akin to how neural circuits process and minimize these discrepancies to refine perception and action. ## 6. **Weighting and Learning Rates** - **Alpha (α):** Represents perceptual uncertainty, impacting how much new information influences belief updates. This can be related to synaptic plasticity where the strength of learning is modulated based on the reliability of the sensory information. - **Eta (η):** Values represent how different categories of inputs are processed, much like how different sensory modalities or contexts might weight information differently in the brain. ## Summary The HGF model provides a neurobiologically plausible framework for understanding how the brain deals with uncertainty and updates beliefs in a dynamic environment. By mirroring the brain's hierarchical, probabilistic, and adaptive capabilities, the model serves as a computational tool to study learning and decision-making processes, focusing on key cognitive and perceptual mechanisms.