Neural manifold connectomics reveals multiregime functional connectivity

Neural activity is organized in low-dimensional structure, yet functional connectivity in fMRI typically represents each brain parcel by a single voxel-averaged time series. This scalar representation makes whole-brain connectivity tractable but discards potentially informative dimensions of within-parcel BOLD activity. Here, we represent each parcel by a low-dimensional temporal subspace derived from its principal-component time series and use the RV coefficient to quantify connectivity between regional subspaces. Across Human Connectome Project resting-state and working-memory data, progressively expanding these subspaces reveals reproducible connectivity regimes with distinct network and identifiability profiles. At rest, connectivity constructed from the first principal component identifies individuals more strongly than either voxel-averaged functional connectivity or higher-dimensional subspace representations. During working memory, identifiability instead peaks after secondary components are included, indicating that the distribution of individual-specific information across the regional PCA spectrum depends on cognitive state. These patterns replicate across independent samples and remain robust across multiple parcellation resolutions. Together, our findings show that within-parcel BOLD structure contains identity- and state-dependent information that is obscured by scalar regional summaries. Functional connectivity may therefore be better understood as a family of related connectomes indexed by the regional subspace retained, providing a general framework for mapping interactions between low-dimensional neural representations.