# Modeling arousal potential of epistemic emotions using Bayesian information gain: Inquiry cycle driven by free energy fluctuations

arXiv: https://arxiv.org/abs/2401.00007 · HTML: https://mlsanity.com/paper/2401.00007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 6 of 6)

- [The free energy principle for action and perception: A mathematical review](https://mlsanity.com/paper/1705.09156/) (2017)
- [Active Inference in Robotics and Artificial Agents: Survey and Challenges](https://mlsanity.com/paper/2112.01871/) (2021)
- [Active Inference for Integrated State-Estimation, Control, and Learning](https://mlsanity.com/paper/2005.05894/) (2020)
- [Information-Theoretic Free Energy as Emotion Potential: Emotional Valence as a Function of Complexity and Novelty](https://mlsanity.com/paper/2003.10073/) (2020)
- [Free energy model of emotional valence in dual-process perceptions](https://mlsanity.com/paper/2210.10262/) (2022)
- [Mathematical Model of Emotional Habituation to Novelty: Modeling with Bayesian Update and Information Theory](https://mlsanity.com/paper/1907.01355/) (2019)

## Built on by (most cited first, 1 of 1)

- [Bayesian Expected Uncertainty Reduction (B-EUR) Model: A Computational Account of What Makes Design Options Worth Trying](https://mlsanity.com/paper/2608.05642/) (2026)

## Abstract (arXiv)

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.