Modeling Arousal Potential of Epistemic Emotions Using Bayesian Information Gain: Inquiry Cycle Driven by Free Energy Fluctuations

Hideyoshi Yanagisawa^*Shimon Honda

• The University of Tokyo, Bunkyo, Japan

Epistemic emotions such as curiosity and interest drive the inquiry process. This study proposes a novel formulation of curiosity and interest using two types of information gain derived from the principle of free energy minimization: Kullback-Leibler divergence (KLD), representing free energy reduction through recognition, and Bayesian surprise (BS), representing free energy reduction via Bayesian update. The conventional Gaussian model predicts infinite divergence of information gain (KLD, BS) as prediction error increases-contradicting the limits of human cognitive resources. The key novelty of this study lies in a simple modification: adding a uniform distribution to the Gaussian likelihood function to model neural activity under large prediction errors. This yields an inverted Ushaped relationship between prediction error and both KLD and BS, producing a finite peak in information gain that better reflects cognitive realism. Based on this convexity, we propose that alternating the maximization of BS and KLD generates an ideal inquiry cycle that fluctuates around the optimal arousal level, with curiosity and interest driving this process. We further analyze how prediction uncertainty (prior variance) and observation uncertainty (likelihood variance) affect the maximum information gain. The results suggest that greater prediction uncertainty (openmindedness) and lower observation uncertainty (attentive observation) promote higher information gains through broader exploration. This mathematical framework integrates the brain's free energy principle with arousal potential theory, offering a unified explanation of the Wundt curve as an information gain function and proposing an ideal, inquiry process driven by epistemic emotions.