GCorP: Global Correlation Pooling

Global covariance pooling summarizes how channel responses vary together. However, it also encodes each channel's scale. Rescaling a channel can therefore change the representation even when the channel relationships are unchanged. We introduce Global Correlation Pooling (GCoRP), which normalizes covariance into a scale-invariant correlation matrix and maps this matrix to geometry-specific flat or hyperbolic coordinates. For flat geometries, we show that non-trivialized correlation-manifold multinomial logistic regression can be optimized exactly in Euclidean coordinates: Riemannian SGD on manifold-valued prototypes and tangent vectors maps to ordinary Euclidean SGD under the induced coordinate map, without tangent-space trivialization. We evaluate GCoRP on image classification, EEG foundation-model classification, and generative-model post-training. Across these tasks, GCoRP offers a favorable accuracy–efficiency trade-off and supports both classification and distribution-matching training.