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The way different perspectives are related to and transform a world model defines a specific perception and imagination scheme. In mathematics, such a collection of transformations corresponds to a \u2018group\u2019, whose \u2018actions\u2019 characterize the geometry of a space. Imbuing world models with a group structure may capture different agents\u2019 spatial awareness and affordance schemes. We used group action as a special class of policies for perspective-dependent control. We explored how such a geometric structure impacts agents\u2019 behaviors, comparing how the Euclidean versus projective groups act on epistemic value in active inference, drive curiosity, and exploration. We formally demonstrate and simulate how the groups induce distinct behaviors in a simple search task. The projective group\u2019s nonlinear magnification of information transformed epistemic value according to the choice of frame, generating behaviors of approach toward objects with uncertain locations due to limited sampling. The Euclidean group had no effect on epistemic value: no action was better than the initial idle state. In structuring a priori an agent\u2019s internal representation, we show how geometry can play a key role in information integration and action planning. Our results add further support to the PCM.<\/jats:p>","DOI":"10.1007\/s00422-024-01001-1","type":"journal-article","created":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T07:05:12Z","timestamp":1737097512000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Action of the Euclidean versus projective group on an agent\u2019s internal space in curiosity driven exploration"],"prefix":"10.1007","volume":"119","author":[{"given":"Gr\u00e9goire","family":"Sergeant-Perthuis","sequence":"first","affiliation":[]},{"given":"Nils","family":"Ruet","sequence":"additional","affiliation":[]},{"given":"Dimitri","family":"Ognibene","sequence":"additional","affiliation":[]},{"given":"Yvain","family":"Tisserand","sequence":"additional","affiliation":[]},{"given":"Kenneth","family":"Williford","sequence":"additional","affiliation":[]},{"given":"David","family":"Rudrauf","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,17]]},"reference":[{"issue":"1360","key":"1001_CR1","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1098\/rstb.1997.0128","volume":"352","author":"RA Andersen","year":"1997","unstructured":"Andersen RA (1997) Multimodal integration for the representation of space in the posterior parietal cortex. 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