Topographic Soft Matching Distance (TSMD): A Framework for Comparing the Spatial Organization of Neural Tuning

Neural populations are spatially organized according to their functional tuning, but how consistently this organization recurs across individuals remains unclear. Existing work typically begins with a predefined tuning variable (e.g., orientation preference, category selectivity), and asks whether its spatial organization appears similar across individuals, often through qualitative comparison of the resulting maps. This becomes limiting for responses to complex natural stimuli, where tuning is high-dimensional and its relevant axes may not be known or easily interpretable. Here, we introduce Topographic Soft-Matching Distance (TSMD), a framework for quantifying shared spatial organization in high-dimensional neural representations without requiring predefined tuning features. TSMD extends soft-matching distance khosla2024soft using fused Gromov–Wasserstein optimal transport, identifying correspondences between neurons that preserve both tuning similarity and relative spatial geometry. It tests for shared topographic organization by varying the relative weighting on matching neurons with similar tuning and preserving pairwise spatial distances, then comparing the resulting matches against a permutation null that shuffles tuning profiles across fixed spatial locations. After validating TSMD on synthetic orientation maps, we apply it to neural recordings across species and cortical areas. We find shared topographic organization across individuals in macaque $\mathrm{V}1$ and $\mathrm{V}4$, but little evidence in mouse $\mathrm{V}1$ or macaque inferotemporal recordings. In human fMRI data collected during naturalistic viewing, TSMD reveals conserved large-scale semantic maps across individuals that cannot be explained by local smoothness alone. Finally, comparisons of developmental models of $\mathrm{V}1$ topography reveal shared global organization across independent realizations of the same self-organizing model despite differences in their precise layouts, but no reliable correspondence beyond local smoothness between models with different map-forming rules. Together, these results establish TSMD as a general framework for testing the conservation of functional topography across brains and computational systems.