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theses

The brain stores a vast amount of information about objects, concepts, and categories. However, how this conceptual knowledge is organized and represented is still subject to avid debate. A central aspect in understanding representations is the notion of similarity. Building on this, two prominent mathematical theories of similarity have made distinct predictions about the structure of mental representations and how to model the psychological space they are stored in. Metric theories (Shepard, 1962; Thurstone, 1927) propose that concepts are represented as points in a continuous metric space (e.g. a vector space) that can be modeled with multidimensional scaling (MDS). Ultrametric theories (Tversky, 1977) propose that concepts are represented as nodes in a connected graph (e.g. a dendrogram), which are modeled using an additive tree (Addtree). We propose a framework in which metric and ultrametric models can be applied to both behavioral and neural data to help characterize properties of conceptual space, such as its structure, shape, and organization. Using this framework, the first aim investigates the metricity of conceptual space by examining whether known metric and ultrametric conceptual spaces (i.e. colors and letters respectively) based on behavioral data can be reproduced from neural data. Contrary to the representations based on behavioral data, we find that the brain represents both colors and letters in a metric space. In the second aim, we explore the geometrical shape of conceptual space using MDS with three large neural datasets, revealing that in all three cases the object representations are stored in a spherical representational space. We successfully verify that the discovered sphericity of the data is not an artifact of the MDS model, suggesting that spherical manifolds might be an intrinsic feature of neural representational space. Based on these results, in the third aim, we experimentally tested the metricity and geometry of subsamples of conceptual space, hypothesizing that they might be metric and spherical as well. Through careful stimulus selection, we created natural categories with an integral (correlated) feature structure and an unnatural Boolean category with separable (uncorrelated) features. Our results show that natural categories are better represented in an ultrametric space and exhibit a conical spiral topology, while the unnatural Boolean category is better represented in a metric space and has no specific topology. Overall, our results reveal that (1) in both brain and behavior, perceptual data is better represented in a metric space, while conceptual data is better represented in an ultrametric space; (2) conceptual spaces based on brain and behavior are not always congruent, and (3) that the brain represents conceptual knowledge in a metric spherical representational space, which (4) contains subcategories that might be ultrametric and are represented in a conical spiral topology. Finally, we discuss reframing concept representation in information theoretical terms, how to embed ultrametric spaces within a metric space, and the relevance of representational flexibility for the organization of concepts.

ETD_11394

Ph.D.

Includes bibliographical references

External ETD doctoral

doi:10.7282/t3-d9z7-yv18

The author owns the copyright to this work.