E.10.INT:4.2 - Recover the model behind the comparison

For surprise, first recover the quantity being used. The surprisal of an observation, -log p(observation), concerns its probability under a selected model. Bayesian surprise concerns the change from prior to posterior beliefs about chosen variables. Expected information gain evaluates a possible observation before it is obtained. A learning-progress signal compares successive predictive or constructive performance under a learning procedure. Those comparisons can disagree, as §5.1 shows.

In active inference, distinguish updating beliefs from selecting actions. Predictive coding uses prediction errors to update beliefs about hidden states and, in learning formulations, model parameters. Policy selection also depends on the information and outcomes expected from action. Recover the prior preferences when a source explains avoiding an outcome through its expected surprise. The source’s account may couple epistemic and pragmatic value. Preserve that coupling together with the quantities and assumptions that give it meaning.

For a Goldilocks region, recover what varies, for which agent and use, and over which range. It might concern an attainable learning challenge, a listener’s response to syncopation or a combination of rhythmic properties. Use the applicable account of the relation between those characteristics and the desired result. The useful region can move as the agent learns or as the task changes. In a search algorithm, a difficulty screen can select candidates for learning while novelty and transfer still govern which possibilities are retained.

When a quantitative answer is needed, C.16 supplies measurement and C.17 separates novelty, usefulness and sample surprise. Keep an adequate qualitative comparison when it already settles the action.