Prediction, error and precision

Predictive coding: the brain as a prediction machine

Predictive coding reframes perception as a process of explaining away sensory input. The brain predicts what it expects to sense, compares that prediction with incoming data, and updates beliefs using precision-weighted prediction errors.

1. From Bayesian updating to prediction error

In the Bayesian updating page, prior beliefs and new evidence combined to form a posterior. Predictive coding expresses a similar idea dynamically: a belief generates a prediction, sensory input provides evidence and the mismatch becomes a prediction error.

$$\varepsilon = y - \hat{y}$$

Here, $y$ is sensory input and $\hat{y}$ is predicted input. When prediction error is large, beliefs may need to change. But the size of the update also depends on precision.

2. Interactive prediction-error update

The dot is the current belief or prediction. The vertical marker is the sensory input. The gap between them is prediction error. Higher precision makes the same error produce a stronger update.

Prediction error 2.60
Precision-weighted error 3.38
Interpretation High precision makes the error more influential, so belief updates are stronger.

3. Precision-weighted prediction error

Predictive coding does not treat all errors equally. An error from a reliable sensory source should matter more than an error from a noisy or uncertain source.

$$\Delta \mu \propto \pi \varepsilon$$

Here, $\mu$ is the belief being updated, $\varepsilon$ is prediction error and $\pi$ is precision. Precision controls the influence of prediction error on belief updating.

4. A simple hierarchy

Predictive coding is usually hierarchical. Higher levels predict lower levels. Lower levels send back errors. Perception emerges from this reciprocal exchange between predictions and prediction errors.

Higher-level belief
hidden cause
prediction ↓
Lower-level sensory input
evidence
prediction error ↑

5. Why this matters for our lab

Predictive coding provides a bridge between symptoms, neural circuits and formal models. Altered synaptic gain, excitation/inhibition balance or neuromodulatory precision can all be framed as changes in how prediction errors are generated, weighted or resolved.

In our work, this connects naturally to Dynamic Causal Modelling, computational psychiatry, pharmacological EEG/MEG and active inference. The same broad logic also underpins embodied intelligence: agents perceive and act by continually reducing uncertainty and prediction error.