  Consider the unsupervised classification problem in random hypergraphs under
the non-uniform \emph{Hypergraph Stochastic Block Model} (HSBM) with two
equal-sized communities ($n/2$), where each edge appears independently with
some probability depending only on the labels of its vertices. In this paper,
an \emph{information-theoretical} threshold for strong consistency is
established. Below the threshold, every algorithm would misclassify at least
two vertices with high probability, and the expected \emph{mismatch ratio} of
the eigenvector estimator is upper bounded by $n$ to the power of minus the
threshold. On the other hand, when above the threshold, despite the information
loss induced by tensor contraction, one-stage spectral algorithms assign every
vertex correctly with high probability when only given the contracted adjacency
matrix, even if \emph{semidefinite programming} (SDP) fails in some scenarios.
Moreover, strong consistency is achievable by aggregating information from all
uniform layers, even if it is impossible when each layer is considered alone.
Our conclusions are supported by both theoretical analysis and numerical
experiments.
