Slow Beats Fast at the Kesten-Stigum Threshold: Minimax, Fisher-Information and Belief-Propagation Characterizations of the Information-Computation Gap in Sparse Stochastic Block Models

תקציר מקורי באנגליתarXiv:2610.08872v1 Announce Type: cross Abstract: We study community recovery in the sparse symmetric stochastic block model with $q$ communities, average degree $d$ and signal strength $\lambda$ through statistical decision theory and Fisher information, and obtain three characterizations of the Kesten-Stigum threshold $d\lambda^2=1$ and of the information-computation gap below it. First, on each community-size profile the minimax risk of any class of rules closed under averaging and vertex relabeling equals its Bayes risk under the uniform prior; the posterior mean is the unique Bayes rule and is admissible, and the Bayes risk of degree-$D$ polynomial rules is the trivial risk times $1-\mathrm{Corr}_D^2$. Combined with known low-degree and information-theoretic results, this gives the ga