  Epistemic emotions, such as curiosity and interest, drive the inquiry
process. This study proposes a novel formulation of epistemic emotions such as
curiosity and interest using two types of information gain generated by the
principle of free energy minimization: Kullback-Leibler divergence(KLD) from
Bayesian posterior to prior, which represents free energy reduction in
recognition, and Bayesian surprise (BS), which represents the expected
information gain by Bayesian prior update. By applying a Gaussian generative
model with an additional uniform likelihood, we found that KLD and BS form an
upward-convex function of surprise (minimized free energy and prediction
error), similar to Berlyne's arousal potential functions, or the Wundt curve.
We consider that the alternate maximization of BS and KLD generates an ideal
inquiry cycle to approach the optimal arousal level with fluctuations in
surprise, and that curiosity and interest drive to facilitate the cyclic
process. We exhaustively analyzed the effects of prediction uncertainty (prior
variance) and observation uncertainty (likelihood variance) on the peaks of the
information gain function as optimal surprises. The results show that greater
prediction uncertainty, meaning an open-minded attitude, and less observational
uncertainty, meaning precise observation with attention, are expected to
provide greater information gains through a greater range of exploration. The
proposed mathematical framework unifies the free energy principle of the brain
and the arousal potential theory to explain the Wundt curve as an information
gain function and suggests an ideal inquiry process driven by epistemic
emotions.
