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Why Adam Can Beat SGD: Second-Moment Normalization Yields Sharper Tails

arXiv – CS AI|Ruinan Jin, Yingbin Liang, Shaofeng Zou|March 4, 2026 at 05:00 AM|1 views

🤖AI Summary

Research paper establishes the first theoretical separation between Adam and SGD optimization algorithms, proving Adam achieves better high-probability convergence guarantees. The study provides mathematical backing for Adam's superior empirical performance through second-moment normalization analysis.

Key Takeaways

→Adam optimizer theoretically proven to outperform SGD with better convergence behavior under bounded variance conditions.
→Study establishes first rigorous theoretical explanation for Adam's superior empirical performance in machine learning applications.
→Adam achieves δ^(-1/2) dependence on confidence parameter versus SGD's δ^(-1) dependence in high-probability guarantees.
→Research uses stopping-time and martingale analysis to distinguish the two optimization methods mathematically.
→Findings bridge the gap between theoretical guarantees and observed empirical performance differences.

#adam-optimizer #sgd #machine-learning #optimization #convergence-analysis #theoretical-research #second-moment #martingale-analysis

Read Original →via arXiv – CS AI

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