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Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations

Announce Type: replace Abstract: In this paper, we propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms by modeling them as first-order integro-differential equations. We perform numerical simulations of these equations, along with stability and convergence analyses, to demonstrate their validity as accurate approximations of the original algorithms. Our results indicate a strong agreement between the behavior of the continuous-time models and the...

arXiv CS 2d ago

Estimating Evolving Functions with Dynamic Gaussian Processes

arXiv:2606.06705v1 Announce Type: new Abstract: This paper develops the Dynamic Gaussian Process (DGP), a framework for estimating functions governed by integro-difference equations (IDEs). IDEs model continuous functions that evolve with discrete-time dynamics and arise naturally from time-discretization of linear partial differential equations (PDEs).

arXiv CS 2d ago