Topographic Soft-Matching Distance (TSMD): A Spatially-Constrained Extension of Soft-Matching

Neural populations are spatially organized according to their functional tuning, but it remains unclear whether this organization constitutes a conserved principle that recurs across individuals. Existing approaches require a predefined tuning variable (\emph{e.g.,} orientation preference) and compare maps qualitatively, which becomes a limiting factor for responses to complex natural stimuli where tuning is high-dimensional, and its relevant axes may not be known \emph{a priori}. Here, we introduce the Topographic Soft-Matching Distance (TSMD), which extends soft-matching via fused Gromov--Wasserstein optimal transport as a method to identify correspondences that preserve both tuning similarity and relative spatial geometry, without requiring predefined tuning features. We test these correspondences against a permutation null that disrupts the tuning--spatial pairing, yielding a statistical test for topographic organization. We validate TSMD on synthetic orientation maps, demonstrating its invariance to rigid transformations and sensitivity to disrupted organization. When applied to single-neuron recordings, TSMD finds little shared organization in mouse $\textrm{V}1$, but strong cross-animal correspondence in macaque $\textrm{V}1$ and $\textrm{V}4$. However, in inferotemporal cortex, topographic structure does not seem to be reliably shared across animals. TSMD thus offers a general approach for quantifying whether spatial organization of neural representations is conserved across individuals and systems.