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cs.LG2024★ 1 cited
Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations
Carlos Heredia
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. W…
hep-th2024
Are nonlocal Lagrangian systems fatally unstable?
Carlos Heredia, Josep Llosa
We prove that higher-derivative and genuinely nonlocal Lagrangian systems can be Lyapunov-stable even when their Hamiltonians lack a lower bound. Explicit free and coupled Pais-Uhl…