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

תקציר מקורי באנגליתarXiv:2609.13920v1 Announce Type: new Abstract: 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 \(\sigma\) the noise standard deviation. We first prove an exact second-moment decomposition for the expected squared distance between any two node representations, yielding the universal lower bound \(2\sigma^2 d\) at every positive time step without contraction or stationarity assumptions.