Stochastic Gumbel graph networks are proposed to learn high-dimensional time series, where the observed dimensions are often spatially correlated. To that end, the observed randomness and spatial-correlations are captured by learning the drift and diffusion terms of the stochastic differential equation with a Gumble matrix embedding, respectively. In particular, this novel framework enables us to investigate the implicit regularization effect of the noise terms in S-GGNs. We provide a theoretical guarantee for the proposed S-GGNs by deriving the difference between the two corresponding loss functions in a small neighborhood of weight. Then, we employ Kuramoto's model to generate data for comparing the spectral density from the Hessian Matrix of the two loss functions. Experimental results on real-world data, demonstrate that S-GGNs exhibit superior convergence, robustness, and generalization, compared with state-of-the-arts.
@article{arxiv.2307.06097,
title = {Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks},
author = {Jin Guo and Ting Gao and Yufu Lan and Peng Zhang and Sikun Yang and Jinqiao Duan},
journal= {arXiv preprint arXiv:2307.06097},
year = {2023}
}