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We study robust community detection in the context of node-corruptedstochastic block model, where an adversary can arbitrarily modify all the edgesincident to a fraction of the $n$ vertices. We present the firstpolynomial-time algorithm that achieves weak recovery at the Kesten-Stigumthreshold even in the presence of a small constant fraction of corrupted nodes.Prior to this work, even state-of-the-art robust algorithms were known to breakunder such node corruption adversaries, when close to the Kesten-Stigumthreshold.  We further extend our techniques to the $Z_2$ synchronization problem, whereour algorithm reaches the optimal recovery threshold in the presence of similarstrong adversarial perturbations.  The key ingredient of our algorithm is a novel identifiability proof thatleverages the push-out effect of the Grothendieck norm of principalsubmatrices.

Reaching Kesten-Stigum Threshold in the Stochastic Block Model under Node Corruptions