Free energy model of emotional valence in dual-process perceptions

An appropriate level of arousal induces positive emotions, and a high arousal potential may provoke negative emotions. To explain the effect of arousal on emotional valence, we propose a novel mathematical framework of arousal potential variations in the dual process of human cognition: automatic and controlled process. Although models have been proposed to explain the emotions in the dual process, a suitable mathematical formulation is largely undiscovered. Our model associates free energy with arousal potential and its variations to explain emotional valence. Decreasing and increasing free energy consequently induces positive and negative emotions, respectively. We formalize a transition from the automatic to controlled process in the dual process as a change of Bayesian prior. We model emotion valence using free-energy increase (FI) when one tries to change one's Bayesian prior and its reduction (FR) when one succeeds to recognize the same stimuli with a changed prior and define three emotions: "interest," "confusion," and "boredom" using the variations. The mathematical analysis comparing between varied Gaussian model parameters suggests that: 1) prediction error (PR) increases FR when the first prior variance is greater than the second prior variance, 2) PR always increases FR, and 3) the distance between priors' means always increases FR. We discuss the association of the outcomes with emotions in the controlled process. The mathematical model provides a general framework for predicting and controlling emotional valence in the dual process that varies with viewpoint and stimuli, as well as for understanding the contradictions in the effects of arousal on the valence.