Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
Two-sample Test of Community Memberships of Weighted Stochastic Block Models
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the same. A test statistic based on singular subspace distance is developed. Under the weighted stochastic block models with dense graphs, the limiting distribution of the proposed test statistic is developed. Simulation results show that the test has correct empirical type 1 errors under the dense graphs. The test also behaves as expected in empirical power, showing gradual changes when the intra-block and inter-block distributions are close and achieving 1 when the two distributions are not so close, where the closeness of the two distributions is characterized by Renyi divergence of order 1/2. The Enron email networks are used to demonstrate the proposed test.
verdicts
UNVERDICTED 2representative citing papers
Proves node subsampling asymptotically approximates joint distribution of network moments under sparse graphon, enabling two-sample tests for unmatchable networks with unequal densities.
citing papers explorer
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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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Multivariate Inference of Network Moments by Subsampling
Proves node subsampling asymptotically approximates joint distribution of network moments under sparse graphon, enabling two-sample tests for unmatchable networks with unequal densities.