arXiv:2411.09734v3 Announce Type: replace Abstract: 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. We perform numerical simulations of these equations, along with stability and convergence analyses, to demonstrate their validity as accurate approximations of the original algorithms. Our results indicate a strong agreement between the behavior of the continuous-time models and the discrete implementations, thus providing a new perspective on the theoretical underst
This research provides a more robust theoretical framework for widely used deep learning optimizers, emerging at a time when AI model complexity demands greater understanding and stability in training processes.
A deeper theoretical understanding of optimization algorithms can lead to more stable, efficient, and generalizable AI models, impacting the pace and reliability of AI development across industries.
The ability to model discrete optimization algorithms with continuous integro-differential equations offers new tools for analysis, potentially enabling more principled algorithm design and theoretical guarantees.
- · AI researchers
- · Deep learning practitioners
- · High-performance computing sector
- · Trial-and-error optimization methods
Improved stability and faster convergence in AI model training.
More reliable deployment of AI systems in critical applications due to better understanding of training dynamics.
Acceleration of research into novel optimization techniques, potentially leading to breakthroughs in AI efficiency and capability.
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