Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909622424567808 |
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| author | Karagoz, Atahan |
| author_facet | Karagoz, Atahan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics Karagoz, Atahan Machine Learning Optimization and Control 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. |
| title | Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2505.19171 |