Extended Data Fig. 1: Embedding-invariant representations on rotational vector fields.
From: MARBLE: interpretable representations of neural population dynamics using geometric deep learning
a Vector fields sampled uniformly at random (n=512) in the interval [−1, 1]2 and fitted with a continuous k-nearest neighbor graph (black lines, k=20). b Embedding-aware joint MARBLE representation of the vector fields using second-order (p=2) gradient filters (rotation-preserving). Each point represents an LFF and points close together represent similar LFFs. Features from the linear vector fields aggregate (clusters 2 and 9), while those from the vortex fields fall on separate halves of a one-dimensional circular manifold corresponding to the one-parameter (angle) variation between them. Black lines show k-means clustering (k=15). c Embedding-agnostic joint MARBLE representations but with rotation-invariant filters. Features from linear fields can no longer be distinguished (cluster 15) because the filter does not preserve rotational information. Features from vortex fields fall on a linear one-dimensional manifold parametrized by the distance from the center. d The histogram of rotation-preserving features can distinguish all fields. e The histogram of rotation-invariant features can discriminate linear fields from vortex fields but not the orientation.
