Going Beyond the Data as the Patching (Sheaving) of Local Knowledge.
Going Beyond the Data as the Patching (Sheaving) of Local Knowledge.
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DOI：
10.3389/fpsyg.2018.01926
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发表时间：
2018
影响因子：
3.8
通讯作者：
Phillips S
中科院分区：
文献类型：
--
作者：
Phillips S
在新的情况下一致地预测结果被通俗地称为“超越数据”或“泛化”。超越了空间和非空间认知中的数据特征，提出了这样一个问题：这些特征是否有一个共同的基础？在这里，我们将这种能力概念化为修补本地知识以获得非本地（全球）信息。追踪从局部性质到整体性质的过程是层理论的范围，层理论是代数和几何/拓扑学之间联系的数学分支。两个认知领域进行了检查：（1）学习线索目标模式，符合一个潜在的代数规则，（2）视觉注意需要整合的空间为基础的功能地图。在这两种情况下，超越数据是从称为“层”的（通用）层理论构造中获得的，即，将局部数据“修补”到拓扑空间，以获得被视为全局一致认知图的表示。这些结果进行了讨论的背景下，以前的（范畴理论）的解释系统性，相对于，类别的普遍结构，沿着与其他认知领域，超越数据是显而易见的。类似于高阶函数（即，接受/返回函数的函数），超越数据作为高阶系统性属性，通过sheaving（高阶（分类）通用构造）来解释。
Consistently predicting outcomes in novel situations is colloquially called “going beyond the data,” or “generalization.” Going beyond the data features in spatial and non-spatial cognition, raising the question of whether such features have a common basis—a kind of systematicity of generalization. Here, we conceptualize this ability as the patching of local knowledge to obtain non-local (global) information. Tracking the passage from local to global properties is the purview of sheaf theory, a branch of mathematics at the nexus of algebra and geometry/topology. Two cognitive domains are examined: (1) learning cue-target patterns that conform to an underlying algebraic rule, and (2) visual attention requiring the integration of space-based feature maps. In both cases, going beyond the data is obtained from a (universal) sheaf theory construction called “sheaving,” i.e., the “patching” of local data attached to a topological space to obtain a representation considered as a globally coherent cognitive map. These results are discussed in the context of a previous (category theory) explanation for systematicity, vis-a-vis, categorical universal constructions, along with other cognitive domains where going beyond the data is apparent. Analogous to higher-order function (i.e., a function that takes/returns a function), going beyond the data as a higher-order systematicity property is explained by sheaving, a higher-order (categorical) universal construction.
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