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Kernel Limit for a Class of Recurrent Neural Networks Trained on Ergodic Data Sequences
Samuel Chun-Hei Lam, Justin Sirignano, Konstantinos Spiliopoulos
Mathematical methods are developed to characterize the asymptotics of recurrent neural networks (RNN) as the number of hidden units, data samples in the sequence, hidden state upda…
Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplers
Benjamin J. Zhang, Youssef M. Marzouk, Konstantinos Spiliopoulos
Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong in…
Quantitative fluctuation analysis of multiscale diffusion systems via Malliavin calculus
Solesne Bourguin, Konstantinos Spiliopoulos
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to…