Free Energy in a Circumplex Model of Emotion (2407.02474v1)

Abstract: Previous active inference accounts of emotion translate fluctuations in free energy to a sense of emotion, mainly focusing on valence. However, in affective science, emotions are often represented as multi-dimensional. In this paper, we propose to adopt a Circumplex Model of emotion by mapping emotions into a two-dimensional spectrum of valence and arousal. We show how one can derive a valence and arousal signal from an agent's expected free energy, relating arousal to the entropy of posterior beliefs and valence to utility less expected utility. Under this formulation, we simulate artificial agents engaged in a search task. We show that the manipulation of priors and object presence results in commonsense variability in emotional states.

• The paper demonstrates how free energy minimization under active inference maps utility differences and belief entropy to model emotional valence and arousal.
• The study employs simulation experiments with agents under varied prior beliefs and search scenarios to trigger distinct emotional responses.
• The findings offer actionable insights for developing artificial systems capable of human-like emotional inference and enhanced interaction.

Free Energy in a Circumplex Model of Emotion

The paper by Pattisapu et al. explores the relationship between free energy minimization within the active inference framework and the emotional states of artificial agents, focusing on integrating both valence and arousal in a Circumplex Model of emotion. The paper aims to provide a comprehensive account of emotions, diverging from previous models which primarily addressed valence while largely overlooking arousal.

Theoretical Background

In the psychological literature, there are two major approaches to the taxonomy of emotions: discrete and dimensional models. Discrete models, such as Ekman's basic emotions model, view emotions as distinct categories like anger, joy, or fear. Dimensional models, exemplified by Russell's Circumplex Model, conceptualize emotions along continuous dimensions of valence (ranging from pleasant to unpleasant) and arousal (ranging from high to low).

The active inference framework, a principle derived from the free energy principle, provides a Bayesian approach to perception and action. Within this framework, an agent minimizes a quantity known as free energy, which can be decomposed into various factors such as accuracy and complexity. Previous active inference formulations, including works by Joffily and Coricelli and Hesp et al., have focused on modeling emotional valence but have not adequately addressed the arousal dimension.

Proposed Model and Emotional Inference

The authors propose a novel approach to mapping emotional states by associating the valence with the utility difference (realized versus expected) and arousal with the entropy of posterior beliefs. Specifically:

• Valence (V): Defined as the difference between the utility of observations and the expected utility. It is formally expressed as:

$Valence = Utility - Expected \, Utility \$

where $Utility = \log P(o_t | C)$ and $$Expected \, Utility = \mathbb{E}_{Q(o_{t}|s_{t-1},\pi)}[\log P(o_t | C)]$$.

• Arousal (A): Related to the entropy $H$ of posterior beliefs:

$$Arousal = \mathbb{E}_{Q(s|o)}[-\log Q(s | o)] = H[Q(s | o)]$$

These dimensions are then mapped onto a Circumplex Model, converting the Cartesian coordinates of valence and arousal into polar coordinates to interpret the agent's emotional states within a two-dimensional circular space.

Simulation Studies

The authors created a series of simulation studies involving an agent tasked with finding an object in a graph-based environment. These scenarios included varying the presence of the object and the agent's prior beliefs about its location. The scenarios were designed to reflect different emotional responses based on the violation or confirmation of the agent's expectations:

1. Uniform Prior: The agent begins with no strong prior and searches until the object is found.
2. Correct Prior: The agent has a precise and correct prior belief about the object location.
3. Incorrect Prior: The agent has a precise but incorrect prior belief.
4. Object Absent - Maybe Here: The agent considers the possibility that the object might not be present.
5. Object Absent - Definitely Here: The agent strongly believes the object must be present and actively searches all locations.

These simulations revealed that agents with correct priors remained calm, while those with incorrect or no priors experienced transitions through various emotional states such as anger or alertness, ultimately finding the object or accepting its absence.

Implications and Future Work

The integration of valence and arousal into a Circumplex Model within the active inference framework provides a nuanced understanding of emotional states. The practical implications are significant for designing artificial intelligent systems capable of more human-like emotional inference and interaction.

Conclusion

By formalizing a comprehensive emotional inference model leveraging both valence and arousal dimensions derived from free energy principles, Pattisapu et al. contribute to the understanding of the emergence of emotions in artificial agents. Future research endeavors should explore the temporal dynamics of these emotional states and extend the framework to multi-agent settings to simulate empathy and other complex social interactions. The implications of this work reach towards creating autonomous systems with more sophisticated, human-like understanding and regulation of emotions.

This essay reflects on the paper's strong theoretical foundation and practical experimentation, grounded in active inference and the Circumplex Model, providing a sophisticated approach to comprehending and simulating emotions in artificial agents.