Influence of the Geometry of the world model on Curiosity Based Exploration

TL;DR

This paper investigates how the geometric structure of an internal world model, specifically Euclidean versus projective groups, influences curiosity-driven exploration and behavior in agents, highlighting the importance of geometry in action planning.

Contribution

It introduces the use of group actions as policies for perspective-dependent control and demonstrates how different geometric structures affect exploration behaviors in agents.

Findings

Projective group induces approach behaviors toward objects of interest.

Euclidean group has no significant effect on epistemic value or exploration.

Geometry of the world model critically influences agent behavior and information integration.

Abstract

In human spatial awareness, 3-D projective geometry structures information integration and action planning through perspective taking within an internal representation space. The way different perspectives are related and transform a world model defines a specific perception and imagination scheme. In mathematics, such collection of transformations corresponds to a 'group', whose 'actions' characterize the geometry of a space. Imbuing world models with a group structure may capture different agents' spatial awareness and affordance schemes. We used group action as a special class of policies for perspective-dependent control. We explored how such geometric structure impacts agents' behavior, comparing how the Euclidean versus projective groups act on epistemic value in active inference, drive curiosity, and exploration behaviors. We formally demonstrate and simulate how the groups induce distinct behaviors in a simple search task. The projective group's nonlinear magnification of information transformed epistemic value according to the choice of frame, generating behaviors of approach toward an object of interest. The projective group structure within the agent's world model contains the Projective Consciousness Model, which is know to capture key features of consciousness. On the other hand, the Euclidean group had no effect on epistemic value : no action was better than the initial idle state. In structuring a priori an agent's internal representation, we show how geometry can play a key role in information integration and action planning.