arXiv:2607.22480 2026 Regularization 1 ideas extracted · analyzed Aug 30, 2026
The paper identifies triangle closure as the leading measurable signature of latent geometry in random graphs. In particular, a geometric graph has a triangle probability exceeding the independent-edge baseline by an amount proportional to p^3 times (log(1/p))^(3/2) divided by sqrt(d), and the signed triangle count appears as the leading likelihood correction. This suggests a graph neural network regularizer based on centered triangle products of learned soft affinities rather than raw triangle density. The centering and density constraint are important because they prevent the model from obtaining the regularization benefit by simply increasing every edge probability.
Add a centered triangle-consistency term to a graph neural network or graph transformer. The term rewards learned edge affinities whose triangle products exceed the independent-edge baseline while preserving the overall edge density, encouraging locally coherent neighborhoods instead of arbitrary pairwise affinities.