pyhgf.updates.vectorised.categorical.vectorised_categorical_prediction_error

pyhgf.updates.vectorised.categorical.vectorised_categorical_prediction_error(layer)

Compute the prediction error of a categorical state node layer.

The value prediction error is the raw residual between the clamped observation (a one-hot pattern) and the softmax prediction:

\[\delta = \mu - \hat{\mu} = \mathrm{one\_hot} - \mathrm{softmax}\]

which is the cross-entropy gradient with respect to the logits. No scaling is needed (the binary layer, by contrast, divides by its Bernoulli variance). The posterior precision is set equal to the expected precision (both one), so the parent’s smoothing gain is exactly one and the routed message is the residual multiplied back through the weights. Categorical leaves carry no volatility level: the volatility fields are left untouched.

Parameters:

layer (LayerState) – Current categorical layer state with mean (the clamped one-hot observation) and expected_mean set by the prediction step.

Returns:

Updated layer state with value_prediction_error and precision set.

Return type:

LayerState