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computational inertia

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Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics

Karagoz, Atahan

arXiv.org Artificial IntelligenceMay-27-2025

We identify a conserved quantity in continuous-time optimization dynamics, termed computational inertia. Defined as the sum of kinetic energy (parameter velocity) and potential energy (loss), this scalar remains invariant under idealized, frictionless training. We formalize this conservation law, derive its analytic decay under damping and stochastic perturbations, and demonstrate its behavior in a synthetic system. The invariant offers a compact lens for interpreting learning trajectories, and may inform theoretical tools for analyzing convergence, stability, and training geometry.

artificial intelligence, computational inertia, machine learning, (14 more...)

arXiv.org Artificial Intelligence

2505.19171

Country: Europe > Switzerland > Basel-City > Basel (0.05)

Genre: Research Report (0.41)

Technology:

Information Technology > Artificial Intelligence > Representation & Reasoning (0.95)
Information Technology > Artificial Intelligence > Machine Learning > Neural Networks > Deep Learning (0.48)

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