Predicting Neural Activity from Connectome Embedding Spaces

Understanding how structured patterns of neural activity emerge from the underlying connectivity is fundamental to elucidating brain function. While cortical connectomes are intrinsically high-dimensional, population activity typically resides in a much lower-dimensional subspace. Consequently, only a small fraction of the information encoded in the connectome appears relevant for shaping activity. Can we identify low-dimensional features of the connectome features be that reliably predict neural activity? Leveraging the MICrONS dataset, which combines millimeter-scale, nanometer-resolution connectivity with simultaneously recorded in-vivo activity, we demonstrate a statistically significant alignment between morphological and functional similarity, quantified by subspace angles and centered kernel alignment. Topological analyses further reveal that the representation spaces of both the connectome and neural activity share a low-dimensional hyperbolic geometry with exponential scaling. These parallels motivated the hypothesis that embedding anatomical affinities into an appropriate geometric space can isolate the functionally relevant features of the connectome. We therefore applied multidimensional scaling to generate such embeddings and trained a simple linear model to reconstruct neuronal activity. Remarkably, the embedded connectome explained $68\%$ in activity similarity, surpassing models that had direct access to activity similarity itself and outperforming similarly simple models that used the full high-dimensional connectome ($56\%$). Our findings uncover a robust structure-function coupling: geometry-aware dimensionality reduction discards much of the connectome's microscopic detail yet yields superior predictions of neural activity. This suggests that synaptic wiring implicitly encodes an abstract, low-dimensional organization that underlies the observed low-dimensional cortical activity.