Catenacci Volpi Nicola, Polani Daniel
School of Engineering and Computer Science, University of Hertfordshire, Hatfield AL109AB, UK.
Entropy (Basel). 2020 Oct 19;22(10):1179. doi: 10.3390/e22101179.
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.
寻求具有一定能力水平的智能体所执行的目标，需要对其世界结构有“理解”。虽然原则上可以根据几何公理对世界结构进行抽象的形式描述，但生物有机体实际采用的表征或生物学上合理的模型应采用的表征，很可能并非如此。相反，我们基于这样的假设开展研究：生物有机体在信息处理能力方面受到限制，过去这一假设催生了许多关于生物学上合理的行为生成的深刻假设和模型。在此，我们运用这种方法来研究通过施加于具身智能体的此类信息约束而出现的各种空间分类。我们将看到，当智能体在用于描述环境中位置的香农信息最小化与由此产生的近似空间描述所产生的位置误差减少之间进行权衡时，就会出现几何丰富的空间表征。此外，智能体并不总是需要从头构建这些表征，而是可以通过完善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，正如信息论中的逐次细化原理所保证的那样，这些在细化的两个步骤中都可以是最优的。最后，通过信息瓶颈方法由这些空间表征诱导出的聚类能够反映环境的拓扑结构，而无需依赖对环境结构的明确几何描述。我们的研究结果表明，自然智能体所拥有的基本几何概念不一定是其先验知识的一部分，而是可能作为节俭处理信息压力的副产品而出现。
