%A Phillips,Steven
%D 2018
%J Frontiers in Psychology
%C
%F
%G English
%K Learning,generalization,Sheaf theory,Presheaf,Sheaf,sheaving,Sheafification,category theory,Functor,Universal
%Q
%R 10.3389/fpsyg.2018.01926
%W
%L
%N 1926
%M
%P
%7
%8 2018-October-09
%9 Conceptual Analysis
%#
%! Going beyond the data
%*
%<
%T Going Beyond the Data as the Patching (Sheaving) of Local Knowledge
%U https://www.frontiersin.org/article/10.3389/fpsyg.2018.01926
%V 9
%0 JOURNAL ARTICLE
%@ 1664-1078
%X 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.