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arXiv · 2602.09101

From Adam to Adam-Like Lagrangians: Second-Order Nonlocal Dynamics

Carlos Heredia
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Abstract

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 model to an existing first-order nonlocal Adam flow through an $\alpha$-refinement limit, and we provide Lyapunov-based stability and convergence analyses. We also introduce an Adam-inspired nonlocal Lagrangian formulation, offering a variational viewpoint. Numerical simulations on Rosenbrock-type examples show agreement between the proposed dynamics and discrete Adam.

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BibTeXRIS

Carlos Heredia. 2026-02-09. From Adam to Adam-Like Lagrangians: Second-Order Nonlocal Dynamics. https://arxiv.org/abs/2602.09101

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