@inproceedings{
sergeant-perthuis2023influence,
title={Influence of the geometry of the feature space on curiosity based exploration},
author={Gr{\'e}goire Sergeant-Perthuis and Nils Ruet and David Rudrauf and Dimitri Ognibene and Yvain Tisserand},
booktitle={NeurIPS 2023 workshop: Information-Theoretic Principles in Cognitive Systems},
year={2023},
url={https://openreview.net/forum?id=Sr2mVydu4r}
}
In human spatial awareness, information appears to be represented according to 3-D projective geometry. It structures information integration and action planning within an internal representation space. 
The way different first person perspectives of an agent relate to each other, through transformations of a world model, defines a specific perception scheme for the agent. This collection of transformations makes a group and it characterizes a geometric space by acting on it. We propose that imbuing world models with a 'geometric' structure, given by a group acting on the space, is one way to capture different perception schemes of agents.
We explore how changing the geometric structure of a world model impacts the behavior of an agent. In particular, we focus on how such geometrical operations transform the formal expression of epistemic value (mutual information), a quantity known in active inference for driving an agent's curiosity about its environment, and the impact on exploration behaviors accordingly. We used group action as a special class of policies for perspective-dependent control. We compared the Euclidean versus projective groups. We formally demonstrate that the groups induce distinct behaviors.
Influence of the geometry of the feature space on curiosity based exploration
Grégoire Sergeant-Perthuis Nils Ruet David Rudrauf Dimitri Ognibene Yvain Tisserand