1 citations · 1 across the 2 of their papers we have counts for
5 papers
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…
Integrable Elasticity via Neural Demand Potentials
Carlos Heredia, Daniel Roncel
We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. The model learns log-demand as a smooth, context-cond…
From Adam to Adam-Like Lagrangians: Second-Order Nonlocal Dynamics
Carlos Heredia
In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal…
Nonlocal Mechanics
Carlos Heredia, Josep Llosa
We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and…
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…