Seeking goals carried out by agents with a level of competency requires an “understanding” of the structure of their world. While abstract formal descriptions of a world structure in terms of geometric axioms can be formulated in principle, it is not likely that this is the representation that is actually employed by biological organisms or that should be used by biologically plausible models. Instead, we operate by the assumption that biological organisms are constrained in their information processing capacities, which in the past has led to a number of insightful hypotheses and models for biologically plausible behaviour generation. Here we use this approach to study various types of spatial categorizations that emerge through such informational constraints imposed on embodied agents. We will see that geometrically-rich spatial representations emerge when agents employ a trade-off between the minimisation of the Shannon information used to describe locations within the environment and the reduction of the location error generated by the resulting approximate spatial description. In addition, agents do not always need to construct these representations from the ground up, but they can obtain them by refining less precise spatial descriptions constructed previously. Importantly, we find that these can be optimal at both steps of refinement, as guaranteed by the successive refinement principle from information theory. Finally, clusters induced by these spatial representations via the information bottleneck method are able to reflect the environment’s topology without relying on an explicit geometric description of the environment’s structure. Our findings suggest that the fundamental geometric notions possessed by natural agents do not need to be part of their a priori knowledge but could emerge as a byproduct of the pressure to process information parsimoniously.

中文翻译：

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空间源于我们所知道的——信息约束引起的空间分类

寻求具有一定能力的代理执行的目标需要“了解”他们的世界结构。虽然原则上可以用几何公理对世界结构进行抽象的形式描述，但这不太可能是生物有机体实际使用的表示，或者生物上合理的模型应该使用的表示。相反，我们假设生物有机体的信息处理能力受到限制，这在过去导致了许多有见地的假设和模型，用于生成生物学上合理的行为。在这里，我们使用这种方法来研究各种类型的空间分类，这些分类是通过对具体代理施加的信息约束而出现的。我们将看到，当智能体在用于描述环境中位置的香农信息的最小化与由此产生的近似空间描述产生的位置误差的减少之间进行权衡时，会出现几何丰富的空间表示。此外，智能体并不总是需要从头开始构建这些表示，但他们可以通过改进先前构建的不太精确的空间描述来获得它们。重要的是，我们发现这些在两个细化步骤中都是最优的，这由信息论的连续细化原理保证。最后，通过信息瓶颈方法由这些空间表示引起的集群能够反映环境的拓扑结构，而无需依赖于环境结构的明确几何描述。我们的研究结果表明，自然代理拥有的基本几何概念不需要成为他们先验知识的一部分，但可能会作为简约处理信息的压力的副产品而出现。