Understanding Why Adam Outperforms SGD: Gradient Heterogeneity in Transformers (2502.00213v2)

Abstract: Transformers 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 transformers by focusing on 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 transformers and show that it is influenced by the placement of layer normalization. Experimental results from fine-tuning transformers in both NLP and vision domains validate our theoretical analyses. This study provides insights into the optimization challenges of transformers and offers guidance for designing future optimization algorithms. Code is available at https://github.com/tom4649/gradient-heterogeneity.

• The paper establishes gradient heterogeneity as the key factor impairing SGD performance in transformer fine-tuning.
• It employs both rigorous theoretical analysis and empirical experiments to show Adam's adaptive, sign-based updates mitigate gradient disparity.
• The findings suggest that targeting gradient heterogeneity in optimizer design could enhance training efficiency for transformer models.

Understanding Why Adam Outperforms SGD: Gradient Heterogeneity in Transformers

This paper addresses the intriguing question of why the Adam optimizer consistently outperforms Stochastic Gradient Descent (SGD) in training transformer models, particularly during the fine-tuning phase. The authors propose that the key differentiating factor is gradient heterogeneity, defined as the disparity in gradient norms among different parameters within the model. This paper not only contributes to a deeper understanding of the optimization dynamics in transformer models but also suggests pathways for designing more effective optimization algorithms.

Gradient Heterogeneity and Optimization Complexity

The paper introduces the concept of gradient heterogeneity as the main factor causing difficulties in optimizing transformer models using SGD. Gradient heterogeneity is quantified by examining the variance of gradient norms across different parameter blocks. Through both theoretical analysis and empirical validation, the authors demonstrate that this heterogeneity negatively impacts the performance of gradient-based optimization methods. On the other hand, Adam's architecture, which incorporates adaptive learning rates and sign-based update mechanisms, is better suited to handle gradient heterogeneity, leading to more efficient convergence.

In deterministic settings, the paper provides upper bounds for iteration complexity, showing that Adam's performance is less sensitive to gradient heterogeneity compared to SGD. This is because sign-based sequences, which are akin to the update strategy used in Adam, are inherently less affected by gradient heterogeneity. The authors also extend the analysis to stochastic settings, concluding that even when noise is present, the fundamental performance gap between Adam and SGD persists due to SGD's heightened sensitivity to gradient heterogeneity.

Transformer Model Architecture Influences

The paper explores the role of architectural features in transformer models, particularly layer normalization, in exacerbating gradient heterogeneity. By analyzing the Jacobians associated with layer normalization in both Pre-LN and Post-LN transformer architectures, the paper finds that Post-LN architectures exhibit more pronounced gradient heterogeneity. This insight emphasizes the need to consider architectural choices when designing and tuning transformer models for optimal performance.

Implications for Momentum in SignSGD

The momentum term in optimization algorithms plays a crucial role in training stability, especially in tasks with many classes, where linear-head parameters can grow excessively. The paper demonstrates that momentum effectively curtails such growth, thereby maintaining stability and preventing erratic parameter updates. This finding highlights the importance of momentum for preventing overabundant bias in sample-wise training scenarios.

Empirical Validation

Through a series of experiments across different tasks in NLP and vision domains, the authors empirically validate their theoretical claims. They observe that transformer models exhibit significant gradient heterogeneity, which is less detrimental to Adam due to its adaptive and sign-based nature. Additionally, the experiments reveal that traditional learning rate schedules fail to compensate for the deficits of SGD in these contexts, reinforcing the inherent advantage of Adam.

Conclusion and Future Directions

This paper significantly advances the understanding of why Adam outperforms SGD, particularly in the field of transformer models. By identifying gradient heterogeneity as a critical factor and elucidating the underlying mechanisms, the paper provides a foundation for the development of future optimization algorithms. It suggests that new algorithms could benefit from incorporating features that mitigate gradient heterogeneity, potentially enhancing the efficiency of training large-scale transformer models. As AI continues to evolve, further exploration into adaptive optimization techniques and architectural innovations will be essential to harness the full potential of transformer models across various applications.