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Optimizer-Induced Low-Dimensional Drift and Transverse Dynamics in Transformer Training

arXiv:2602.23696v1 Announce Type: new Abstract: We study the geometry of training trajectories in small transformer models and find that parameter updates organize into a dominant drift direction with transverse residual dynamics. Using uncentered, row-normalized trajectory PCA, we show that a single direction captures a large fraction of cumulative parameter movement early in training, while remaining components encode oscillatory behavior in auxiliary probe performance. Instantaneous gradients exhibit little alignment with this dominant direction, indicating that it arises from accumulated optimizer updates rather than per-batch gradient structure. Comparing AdamW with SGD variants at matched loss levels reveals substantial differences in trajectory geometry: AdamW develops multi-dimensional drift structure, whereas SGD-family optimizers produce nearly colinear parameter evolution and weaker probe dynamics. Reheating selectively perturbs transverse components with minimal effect on

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Yongzhong Xu · · 1 min read · 11 views
#cs.LG #cs.AI

arXiv:2602.23696v1 Announce Type: new Abstract: We study the geometry of training trajectories in small transformer models and find that parameter updates organize into a dominant drift direction with transverse residual dynamics. Using uncentered, row-normalized trajectory PCA, we show that a single direction captures a large fraction of cumulative parameter movement early in training, while remaining components encode oscillatory behavior in auxiliary probe performance. Instantaneous gradients exhibit little alignment with this dominant direction, indicating that it arises from accumulated optimizer updates rather than per-batch gradient structure. Comparing AdamW with SGD variants at matched loss levels reveals substantial differences in trajectory geometry: AdamW develops multi-dimensional drift structure, whereas SGD-family optimizers produce nearly colinear parameter evolution and weaker probe dynamics. Reheating selectively perturbs transverse components with minimal effect on the dominant drift coordinate. These findings suggest that optimizer choice shapes the effective dimensionality and structure of learning trajectories beyond what is apparent from loss values alone.

Executive Summary

The article 'Optimizer-Induced Low-Dimensional Drift and Transverse Dynamics in Transformer Training' explores the geometry of training trajectories in small transformer models, shedding light on the impact of optimizer choice on effective dimensionality and structure of learning trajectories. Utilizing uncentered, row-normalized trajectory PCA, the authors reveal a dominant drift direction with transverse residual dynamics, which arises from accumulated optimizer updates rather than per-batch gradient structure. The study compares AdamW with SGD variants, demonstrating substantial differences in trajectory geometry and suggesting that optimizer choice plays a crucial role in shaping the learning process. The findings have significant implications for the optimization of transformer models and the development of more effective training strategies.

Key Points

  • ▸ Parameter updates in transformer models organize into a dominant drift direction with transverse residual dynamics.
  • ▸ The dominant drift direction arises from accumulated optimizer updates rather than per-batch gradient structure.
  • ▸ Optimizer choice significantly impacts the effective dimensionality and structure of learning trajectories.

Merits

Strength

The study provides a comprehensive analysis of transformer model training trajectories, revealing insights into the impact of optimizer choice on the learning process.

Methodological Rigor

The authors employ a robust methodological approach, utilizing uncentered, row-normalized trajectory PCA to analyze the geometry of training trajectories.

Implications for Optimization

The findings have significant implications for the optimization of transformer models and the development of more effective training strategies.

Demerits

Limitation

The study is limited to small transformer models and may not generalize to larger models or more complex tasks.

Scope of Analysis

The analysis focuses primarily on the impact of optimizer choice and may not consider other factors that influence the learning process.

Expert Commentary

The article 'Optimizer-Induced Low-Dimensional Drift and Transverse Dynamics in Transformer Training' provides a significant contribution to the field of natural language processing and machine learning, shedding light on the impact of optimizer choice on the learning process. The authors' use of uncentered, row-normalized trajectory PCA to analyze the geometry of training trajectories is a robust and methodologically sound approach. The findings have significant implications for the optimization of transformer models and the development of more effective training strategies. However, the study is limited to small transformer models and may not generalize to larger models or more complex tasks. Nevertheless, the analysis provides valuable insights into the behavior of transformer model training trajectories and can inform the development of more efficient training strategies.

Recommendations

  • ✓ Future research should focus on exploring the generalizability of the findings to larger transformer models and more complex tasks.
  • ✓ Researchers should prioritize the development of more effective optimization techniques that take into account the accumulated optimizer updates that drive the dominant drift direction.

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