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

arXiv: https://arxiv.org/abs/2304.00188 · HTML: https://mlsanity.com/paper/2304.00188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 17 of its 95 references that are in the map.
- First posted on arXiv 1 Apr 2023.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 17 of 17)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Learning First-Order Symbolic Representations for Planning from the Structure of the State Space](https://mlsanity.com/paper/1909.05546/) (2019)
- [Geometric Entropic Exploration](https://mlsanity.com/paper/2101.02055/) (2021)
- [Path integrals, particular kinds, and strange things](https://mlsanity.com/paper/2210.12761/) (2022)
- [The Mathematical Structure of Integrated Information Theory](https://mlsanity.com/paper/2002.07655/) (2020)
- [Graph-Based Topological Exploration Planning in Large-Scale 3D Environments](https://mlsanity.com/paper/2103.16829/) (2021)
- [Proactive Intention Recognition for Joint Human-Robot Search and Rescue Missions through Monte-Carlo Planning in POMDP Environments](https://mlsanity.com/paper/1908.10125/) (2019)
- [On Non-Linear operators for Geometric Deep Learning](https://mlsanity.com/paper/2207.03485/) (2022)
- [Mysteries of Visual Experience](https://mlsanity.com/paper/1604.08612/) (2016)
- [Exploratory State Representation Learning](https://mlsanity.com/paper/2109.13596/) (2021)
- [The Moon Illusion explained by the Projective Consciousness Model](https://mlsanity.com/paper/1809.04414/) (2018)
- [Modeling the subjective perspective of consciousness and its role in the control of behaviours](https://mlsanity.com/paper/2012.12963/) (2020)
- [Combining the Projective Consciousness Model and Virtual Humans to assess ToM capacity in Virtual Reality: a proof-of-concept](https://mlsanity.com/paper/2104.07053/) (2021)

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

- [Pose-Aware Self-Supervised Learning with Viewpoint Trajectory Regularization](https://mlsanity.com/paper/2403.14973/) (2024)

## Abstract (arXiv)

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.