Persistence of map-induced structure under t-SNE gradient flow

Determine whether the weak limit as $t\to\infty$ of a t-SNE gradient flow remains induced by a measurable map when the initial symmetry-invariant coupling is induced by a measurable map.

Background

The generalized t-SNE formulation allows optimization over couplings, or plans, rather than only deterministic maps. This relaxation facilitates compactness and variational analysis but permits a single feature-space point to correspond to multiple embedded locations.

The authors note that map-induced structure is important for interpreting embeddings and that the conjecture is needed to turn symmetry-invariant critical points in the relaxed coupling formulation into critical points represented by genuine embeddings.