Fast convergence rate of values with strong convergence of trajectories via inertial dynamics with Tikhonov regularization terms and asymptotically vanishing damping
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Bibliographic record
Abstract
In a Hilbert space H , we investigate the long time behavior of the trajectories of the following second-order differential system (t)and the time scale parameter is a positive function that tends to infinity as time approaches infinity.We based on Tikhonov regularization techniques and an appropriate Lyapunov energy function simultaneously prove fast convergence rates of the objective function to the global minimum, strong convergence of trajectories to the minimizer of the minimum norm, as well as convergence rates for the velocity and the gradient.Numerical examples are also given to illustrate these results.Finally, we extend our results to the non-smooth case.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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