Yifei E. Chen^1,2 (evchen@uchicago.edu), Andrew J. Stier³, Marc G. Berman^1,4, Wilma A. Bainbridge^1,2,4; ¹University of Chicago, ²Institute for Mind and Biology, ³Santa Fe Institute, ⁴Neuroscience Institute

Understanding the geometry underlying neural representational spaces for complex visual knowledge is essential for explaining how the brain organizes information. Most representational frameworks assume a Euclidean geometry, inherited from linear encoding models and classical multidimensional scaling (MDS). Yet, recent work (Lee et al., preprint) showed that human similarity judgments exhibit hyperbolic-like curvature, motivating the hypothesis that neural representations themselves may be better captured in non-Euclidean spaces. Here, we present the first fMRI pipeline for systematically evaluating Euclidean versus hyperbolic geometry within a region-of-interest (ROI) parcellation scheme. Using the THINGS-fMRI dataset (Hebart et al., 2023), we constructed concept-level neural representational dissimilarity matrices (RDMs) for each Harvard–Oxford region by averaging voxel-wise responses across stimuli belonging to the same concept. We then applied ALBATROSS (Stier et al., preprint), a persistent-homology method that infers each model’s optimal dimensionality by minimizing topological divergence. For each ROI, Euclidean and hyperbolic candidate models were compared using a χ² divergence metric integrating three measures: Integrated Betti Value (IBV), L1 distance, and Wasserstein-1 (W1). Next, we generated embeddings using geometry-appropriate MDS and assessed model fidelity with stress (global metric preservation) and Spearman rank fidelity (relative-distance preservation). Hyperbolic advantages were evident across posterior temporal and parietal association cortices involved in high-level visual processing and semantic integration—regions where object representations become relational and conceptually structured. More broadly, hyperbolic embeddings yielded lower stress across nearly all ROIs, indicating a superior global geometric fit to empirical neural dissimilarities. In contrast, Euclidean and hyperbolic embeddings exhibited similar Spearman rank fidelity, suggesting that both spaces preserve local ordering of representational distances to a comparable degree. Together, this pipeline provides a principled, geometry-aware framework for testing whether neural representations exhibit Euclidean or hyperbolic structure, opening new possibilities for mechanistic modeling and the discovery of representational principles that may be invisible under traditional Euclidean assumptions.