Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model

• URL: http://arxiv.org/abs/2604.20907v1
• Date: Tue, 21 Apr 2026 20:43:10 GMT
• Title: Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model
• Abstract summary: We study the community detection problem in the non-uniform hypergraph block model.<n>Can multiple uniform hypergraph layers below the detection threshold be combined to enable weak recovery?<n>We show that weak recovery is possible whenever the sum of signal-to-noise ratios across all uniform hypergraph layers exceeds one.
• Score: 8.513101411060898
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the community detection problem in the non-uniform hypergraph stochastic block model (HSBM), where hyperedges of varying sizes coexist. This setting captures higher-order and multi-view interactions and raises a fundamental question: can multiple uniform hypergraph layers below the detection threshold be combined to enable weak recovery? We answer this question by establishing a Kesten--Stigum-type bound for weak recovery in a general class of non-uniform HSBMs with $r$ blocks, generated according to multiple symmetric probability tensors. In the case $r=2$, we show that weak recovery is possible whenever the sum of the signal-to-noise ratios across all uniform hypergraph layers exceeds one, thereby confirming the positive part of a conjecture in (Chodrow et al., 2023). Moreover, we provide a polynomial-time spectral algorithm that achieves this threshold via an optimally weighted non-backtracking operator. For the unweighted non-backtracking matrix, our spectral method attains a different algorithmic threshold, also conjectured in (Chodrow et al., 2023). Our approach develops a spectral theory for weighted non-backtracking operators on non-uniform hypergraphs, including a precise characterization of outlier eigenvalues and eigenvector overlaps. We introduce a novel Ihara--Bass formula tailored to weighted non-uniform hypergraphs, which yields an efficient low-dimensional representation and leads to a provable spectral reconstruction algorithm. Taken together, these results provide a principled and computationally efficient approach to clustering in non-uniform hypergraphs, and highlight the role of optimal weighting in aggregating heterogeneous higher-order interactions.

Related papers

• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Almost Asymptotically Optimal Active Clustering Through Pairwise Observations [59.20614082241528]
  We propose a new analysis framework for clustering $M$ items into an unknown number of $K$ distinct groups using noisy and actively collected responses.<n>We establish a fundamental lower bound on the expected number of queries needed to achieve a desired confidence in the accuracy of the clustering.<n>We develop a computationally feasible variant of the Generalized Likelihood Ratio statistic and show that its performance gap to the lower bound can be accurately empirically estimated.
  arXiv  Detail & Related papers  (2026-02-05T14:16:47Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Information-Theoretic Limits and Strong Consistency on Binary Non-uniform Hypergraph Stochastic Block Models [0.0]
  unsupervised classification problem in random hypergraphs under the non-uniform Hypergraph the Block Model (HSBM)<n>In this paper, the information-theoretic limits on the clustering accuracy and the strong consistency threshold are established.
  arXiv  Detail & Related papers  (2023-06-12T03:38:25Z)
• Optimal and exact recovery on general non-uniform Hypergraph Stochastic Block Model [0.0]
  We consider the community detection problem in random hypergraphs under the non-uniform hypergraphinger block model (HSBM) We establish, for the first time in the literature, a sharp threshold for exact recovery under this non-uniform case, subject to minor constraints. We provide two efficient algorithms which successfully achieve exact recovery when above the threshold, and attain the lowest possible ratio when the exact recovery is impossible.
  arXiv  Detail & Related papers  (2023-04-25T20:30:33Z)
• Nonbacktracking spectral clustering of nonuniform hypergraphs [2.408714894793063]
  We study spectral clustering for nonuniform hypergraphs based on the hypergraph nonbacktracking operator. We propose an alternating algorithm for inference in a hypergraph blockmodel via linearized belief-propagation.
  arXiv  Detail & Related papers  (2022-04-27T01:14:06Z)
• Sparse random hypergraphs: Non-backtracking spectra and community detection [10.503525445174464]
  We prove that a spectral method based on the non-backtracking operator for hypergraphs works with high probability down to the generalized Kesten-Stigum detection threshold conjectured by Angelini et al. This is the first provable and efficient algorithm that achieves the conjectured threshold for HSBMs with $r$ blocks generated according to a general symmetric probability tensor.
  arXiv  Detail & Related papers  (2022-03-14T17:45:03Z)
• Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model [6.681901523019242]
  We consider the community detection problem in random hypergraphs under the nonuniform hypergraph block model (HSBM) We provide a spectral algorithm that outputs a partition with at least a $gamma$ fraction of the vertices classified correctly, where $gammain depends on the signal-to-noise ratio (SNR) of the model. The theoretical analysis of our algorithm relies on the concentration and regularization of the adjacency matrix for non-uniform random hypergraphs, which can be of independent interest.
  arXiv  Detail & Related papers  (2021-12-22T05:38:33Z)
• Exact Recovery in the General Hypergraph Stochastic Block Model [92.28929858529679]
  This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph block model (d-HSBM) We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below it.
  arXiv  Detail & Related papers  (2021-05-11T03:39:08Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.