12. A Mathematical Model of Emotions for Novelty

This chapter discusses a mathematical model of emotions associated with novelty at variable uncertainty levels. The model predicts dominant emotion dimensions, arousal (intensity of emotion), and valence (positivity or negativity). To represent the arousal level, we used Kullback–Leibler divergence of Bayesian posterior from the prior, which we termed information gain. The information gain corresponds to surprise, a high-arousal emotion, upon experiencing a novel event. Based on Berlyne’s hedonic function (or the inverse U-shaped curve, so-called Wundt curve), we formalized valence as a summation of reward and aversion systems that are modeled as sigmoid functions of information gain. We derived information gain as a function of prediction errors (i.e., differences between the prediction and the reality), uncertainty (i.e., variance of the prior that is proportional to prior entropy), and sensory noise. This functional model predicted an interaction effect of prediction errors and uncertainty on information gain, which we termed the arousal crossover effect. Our model’s predictions of arousal help identify positively accepted novelty.