Understanding Why Adam Outperforms SGD: Gradient Heterogeneity in Transformers

Transformer models are challenging to optimize with SGD and typically require adaptive optimizers such as Adam. However, the reasons behind the superior performance of Adam over SGD remain unclear. In this study, we investigate the optimization of transformer models by focusing on \emph{gradient heterogeneity}, defined as the disparity in gradient norms among parameters. Our analysis shows that gradient heterogeneity hinders gradient-based optimization, including SGD, while sign-based optimization, a simplified variant of Adam, is less affected. We further examine gradient heterogeneity in transformer models and show that it is influenced by the placement of layer normalization. Additionally, we show that the momentum term in sign-based optimization is important for preventing the excessive growth of linear-head parameters in tasks with many classes. Experimental results from fine-tuning transformer models in both NLP and vision domains validate our theoretical analyses. This study provides insights into the optimization challenges of transformer models and offers guidance for designing future optimization algorithms. Code is available at \url{https://github.com/tom4649/gradient-heterogeneity}.