Precision-Weighted Prediction Error
Precision-weighted prediction error is the fundamental currency of neural computation in predictive processing and the Free Energy Principle. It is the discrepancy between predicted and observed signals, scaled by the brain's confidence in its own predictions.
Formally, if $\epsilon$ is raw prediction error and $\pi$ is precision (inverse variance), the precision-weighted error is $\pi \cdot \epsilon$. High precision means the error is treated as reliable signal; low precision means it is treated as noise.
This mechanism explains how the brain balances sensitivity and stability: it updates beliefs aggressively when confident in its predictions, and conservatively when uncertain. Dopamine is thought to encode precision-weighted prediction error, regulating learning rates and action selection.