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.

This study extends the mathematical model of emotion dimensions that we previously proposed (Yanagisawa, et al. 2019, Front Comput Neurosci) to consider perceived complexity as well as novelty, as a source of arousal potential. Berlyne's hedonic function of arousal potential (or the inverse U-shaped curve, the so-called Wundt curve) is assumed. We modeled the arousal potential as information contents to be processed in the brain after sensory stimuli are perceived (or recognized), which we termed sensory surprisal. We mathematically demonstrated that sensory surprisal represents free energy, and it is equivalent to a summation of information gain (or information from novelty) and perceived complexity (or information from complexity), which are the collative variables forming the arousal potential. We demonstrated empirical evidence with visual stimuli (profile shapes of butterfly) supporting the hypothesis that the summation of perceived novelty and complexity shapes the inverse U-shaped beauty function. We discussed the potential of free energy as a mathematical principle explaining emotion initiators.

Creativity is one of the great challenges for machine intelligence. There is no shortage of evidence showing how machines can match and even outperform humans in vast areas of endeavor, such as face and object recognition, doodling, image synthesis, language translation, a vast variety of games such as chess and Go, and so on. But when it comes to creativity, the machines lag well behind. For example, machines have learned to recognize artistic style, separate it from the content of an image, and then apply it to other images. That makes it possible to convert any photograph into the style of Van Gogh's Starry Night, for instance.