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

1. 1Understand the classical bounded variance model and its limitations in explaining Adam's empirical performance
2. 2Develop a stopping-time/martingale analysis to distinguish Adam from SGD
3. 3Recognize the role of second-moment normalization in Adam's faster convergence
4. 4Apply the insights to optimize model training and hyperparameter tuning

Machine learning researchers and engineers can benefit from understanding the theoretical advantages of Adam over SGD, leading to improved model training and convergence

💡 Second-moment normalization in Adam leads to sharper tails in the loss landscape, explaining its faster empirical convergence

🚀 Adam beats SGD due to second-moment normalization! 🤔