# Fundamental limits of community detection from multi-view data: multi-layer, dynamic and partially labeled block models

arXiv: https://arxiv.org/abs/2401.08167 · HTML: https://mlsanity.com/paper/2401.08167/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 69 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Graph-based Approximate Message Passing Iterations](https://mlsanity.com/paper/2109.11905/) (2021)
- [Contextual Stochastic Block Model: Sharp Thresholds and Contiguity](https://mlsanity.com/paper/2011.09841/) (2020)
- [General Community Detection with Optimal Recovery Conditions for Multi-relational Sparse Networks with Dependent Layers](https://mlsanity.com/paper/2004.03480/) (2020)
- [Approximate Message Passing for the Matrix Tensor Product Model](https://mlsanity.com/paper/2306.15580/) (2023)
- [Semi-supervised Community Detection via Structural Similarity Metrics](https://mlsanity.com/paper/2306.01089/) (2023)

## Built on by (most cited first, 7 of 7)

- [Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods](https://mlsanity.com/paper/2405.13912/) (2024)
- [Efficient Graph Matching for Correlated Stochastic Block Models](https://mlsanity.com/paper/2412.02661/) (2024)
- [Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares](https://mlsanity.com/paper/2510.17561/) (2025)
- [Optimal thresholds and algorithms for a model of multi-modal learning in high dimensions](https://mlsanity.com/paper/2407.03522/) (2024)
- [Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning](https://mlsanity.com/paper/2602.04872/) (2026)
- [Fundamental Limits of Community Detection in Contextual Multi-Layer Stochastic Block Models](https://mlsanity.com/paper/2602.08173/) (2026)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)

## Abstract (arXiv)

Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy partial labeling of vertices etc. We study community detection in these disparate settings via a unified theoretical framework, and investigate the fundamental thresholds for community recovery. We characterize the mutual information between the data and the latent parameters, provided the degrees are sufficiently large. Based on this general result, (i) we derive a sharp threshold for community detection in an inhomogeneous multilayer block model citepchen2022global, (ii) characterize a sharp threshold for weak recovery in a dynamic stochastic block model citepmatias2017statistical, and (iii) identify the limiting mutual information in an unbalanced partially labeled block model. Our first two results are derived modulo coordinate-wise convexity assumptions on specific functions -- we provide extensive numerical evidence for their correctness. Finally, we introduce iterative algorithms based on Approximate Message Passing for community detection in these problems.