Sergeant-Perthuis Grégoire, Ruet Nils, Ognibene Dimitri, Tisserand Yvain, Williford Kenneth, Rudrauf David
LCQB Sorbonne Université & OURAGAN team, Inria Paris Paris, France.
CIAMS, Université Paris-Saclay, Orsay & Université d'Orléans, Orléans, France.
Biol Cybern. 2025 Jan 17;119(1):4. doi: 10.1007/s00422-024-01001-1.
According to the Projective Consciousness Model (PCM), in human spatial awareness, 3-dimensional projective geometry structures information integration and action planning through perspective taking within an internal representation space. 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 '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 a geometric structure impacts agents' 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's 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's 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.
根据投射意识模型（PCM），在人类空间意识中，三维投射几何通过在内部表征空间中进行视角采择来构建信息整合和行动规划。不同视角与世界模型相关联并对其进行转换的方式定义了一种特定的感知和想象模式。在数学中，这样一组变换对应于一个“群”，其“作用”刻画了空间的几何特征。赋予世界模型以群结构可能会捕捉不同主体的空间意识和可供性模式。我们将群作用用作一类特殊的依赖视角控制的策略。我们探究了这种几何结构如何影响主体的行为，比较了欧几里得群和投射群在主动推理中对认知价值的作用方式、激发好奇心以及探索行为。我们正式论证并模拟了这些群在一个简单搜索任务中如何引发不同的行为。投射群对信息的非线性放大根据框架的选择改变了认知价值，由于采样有限，产生了朝向位置不确定物体的趋近行为。欧几里得群对认知价值没有影响：不采取行动比初始的闲置状态更好。在对主体的先验内部表征进行构建时，我们展示了几何如何在信息整合和行动规划中发挥关键作用。我们的结果为PCM提供了进一步的支持。
