Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs

What the math gives to ML

The paper provides non-asymptotic spectral control for sparse threshold graphs whose edges are dependent because they share high-dimensional latent vectors. This suggests using a thresholded similarity graph as a sparse geometric surrogate for dense pairwise attention, with its leading eigenspace supplying a compact latent-coordinate feature. The concentration scale gives an actionable diagnostic for whether the spectral representation is likely to contain signal rather than graph noise. The most direct experiment is a sparse attention or graph encoder that compares this spectral geometry against ordinary top-k similarity sparsification at matched edge count and compute.