Why it is a question
THEORY-228 now states HaoChen, Wei, Gaidon and Ma’s Theorem 3.8 on a finite augmentation space. At the population optimum of the spectral contrastive loss, linear-probe error is bounded, up to constant and logarithmic factors, by the label-recovery error α over the squared sparsest-partition conductance. Two things the former promote_when asked for remain undone.
First, the paper’s App. F proves only that an eigenbasis exists off a finite space, under a uniform bound on the density ratio, and asserts the extension of Theorems 3.8, 4.2 and 4.3 with the proof omitted. Second, α, the conductance ρ and the eigengap are measured on no real dataset, so nothing shows the bound is below 1 anywhere.
What would answer it
A written-out proof of the guarantee on a general augmentation space, under a stated integrability condition, would answer the first half yes. A measurement of α and ρ on a real augmentation graph, or on a faithful proxy, giving a bound below trivial would answer the second half yes. A finite augmentation graph that meets Assumptions 3.6 and 3.7 but whose population spectral minimiser has probe error above the bound would refute the theorem itself. What cannot settle it: linear-probe accuracies of trained networks, since the theorem is about the population minimiser.