6 papers
Concentration of Regularized Sparse Random Matrices: Spectral Edge Bounds via Nonbacktracking Operators
Hai-Xiao Wang
In sparse random matrices, spectral outliers (eigenvalues and singular values located away from the bulk) emerge due to degree fluctuations: high degrees inflate the operator norm,…
Majority Dynamics on Resampled Sparse Erdős--Rényi Graphs: Gaussian Winner Selection in Collaborative Agent Networks
Ioana Dumitriu, Muchen Ju, Hai-Xiao Wang
Collective decisions in agent networks emerge from repeated local interactions, as agents update their opinions (colors) based on their neighbors, potentially leading to consensus.…
Majority Dynamics on Assortative Sparse Stochastic Block Models
Ioana Dumitriu, Muchen Ju, Hai-Xiao Wang
Majority dynamics is a two-opinion process in which each vertex repeatedly updates to the majority opinion among its neighbors. We study this process on a resampled sparse binary s…
Attention Mechanisms Through the Lens of Numerical Methods: Approximation Methods and Alternative Formulations
Michel Fabrice Serret, Alice Cortinovis, Yijun Dong +10
The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale i…
Singular values of sparse random rectangular matrices: Emergence of outliers at criticality
Ioana Dumitriu, Hai-Xiao Wang, Zhichao Wang +1
Consider the random bipartite Erdős-Rényi graph , where each edge with one vertex in and the other vertex in is connected with probabi…
Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks
Hai-Xiao Wang, Zhichao Wang
We delve into the challenge of semi-supervised node classification on the Contextual Stochastic Block Model (CSBM) dataset. Here, nodes from the two-cluster Stochastic Block Model…