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

Grégoire Sergeant-Perthuis (1, 2) , Nils Ruet (3) , David Rudrauf (3) , Dimitri Ognibene (4) , Yvain Tisserand (5)

1 LCQB-AG - Analytical Genomics [LCQB]
2 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
3 CIAMS - Complexité, Innovation, Activités Motrices et Sportives
4 Dipartimento di Psicologia
5 CISA - Swiss Center for Affective Sciences

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 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 \textit{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 consciousnes. On the other hand, the Euclidean group had no effect on epistemic value : no action was better than the initial idle state. In structuring \textit{a priori} an agent’s internal representation, we show how geometry can play a key role in information integration and action planning.

Mots clés: Curiosity; Mathematical Consciousness; Intentionality; Spatial Cognition; Geometric world model Exploration Embodied Cognitive Science Cognitive Modeling Perception-Action Coupling; Geometric world model; Exploration; Embodied Cognitive Science; Cognitive Modeling; Perception-Action Coupling

Domaines: Intelligence artificielle [cs.AI]; Sciences cognitives; Sciences de l'ingénieur [physics]

Grégoire Sergeant-Perthuis, Nils Ruet, David Rudrauf, Dimitri Ognibene, Yvain Tisserand. Influence of the Geometry of the world model on Curiosity Based Exploration. 2024. ⟨hal-04054736v2⟩