Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks

• URL: http://arxiv.org/abs/2307.06097v1
• Date: Wed, 12 Jul 2023 11:38:34 GMT
• Title: Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks
• Abstract summary: Gumbel graph networks are proposed to learn high-dimensional time series. We show that S-GGNs exhibit superior convergence, robustness, and generalization, compared with state-of-the-arts networks.
• Score: 5.374505641331418
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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