arXiv:2603.09581v2 Announce Type: replace Abstract: Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near 1 for convergence, this work investigates the ``natural'' auto-convergence properties of Adam. We identify a class of highly degenerate polynomials where Adam converges automatically without additional schedulers. Specifically, we derive theoretical conditions for local asymptotic stability on degenerate po
Ongoing advancements in AI and deep learning research continue to require deeper theoretical understanding of optimization algorithms as models become larger and more complex.
Understanding the fundamental convergence properties of algorithms like Adam can lead to more efficient training, better model performance, and reduced computational costs in AI development.
This research contributes to a more robust theoretical foundation for Adam, potentially reducing the need for heuristic tuning and improving its reliability in specific, challenging optimization landscapes.
- · AI researchers
- · Deep learning practitioners
- · Cloud computing providers (through efficiency gains)
Improved understanding of Adam's behavior allows for more targeted application and hyperparameter selection.
Optimized training processes could accelerate the development and deployment of complex AI models across various sectors.
Reduced computational overhead for training could subtly lower barriers to entry for AI model development, democratizing access to advanced AI capabilities over time.
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Read at arXiv cs.LG