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Finite-Time Node Separation in Recurrent Graph Neural Networks with Persistent Gaussian Perturbations

arXiv · AI, language, vision and robotics · article · Sep 12, 2026 · UTC

Persistent Gaussian perturbations have been shown to prevent asymptotic oversmoothing in recurrent Graph Neural Networks (GNNs) by ensuring a positive stationary Dirichlet energy. However, this global energy bound does not guarantee that individual node representations remain distinct at finite depths. In this paper, we provide a complementary finite-time analysis of the same persistent-noise architecture. Let \(d\) denote the representation dimension and \(σ\) the noise standard deviation. We first prove an exact second-moment decomposition for the expected squared distance between any two no

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