Gradient-Direction Sensitivity Reveals Linear-Centroid Coupling Hidden by Optimizer Trajectories
📰 ArXiv cs.AI
Discover how gradient-direction sensitivity reveals hidden linear-centroid coupling in optimizer trajectories, improving diagnostic accuracy by 1-2 orders of magnitude
Action Steps
- Perform rolling SVD on loss gradients instead of AdamW updates to increase diagnostic accuracy
- Apply the Linear Centroid Hypothesis (LCH) to identify features coupled with SED directions
- Compare the measured perturbative coupling between SED directions and LCH features using different SVD methods
- Analyze the results to understand how gradient-direction sensitivity affects optimizer trajectories
- Use this insight to improve the development of optimizers and their application in machine learning models
Who Needs to Know This
Machine learning researchers and engineers working on optimizer development and analysis can benefit from this knowledge to improve their models' performance and understanding of optimizer behavior
Key Insight
💡 Replacing rolling SVD of AdamW updates with rolling SVD of loss gradients significantly increases the measured perturbative coupling between SED directions and LCH features
Share This
💡 Gradient-direction sensitivity reveals hidden linear-centroid coupling in optimizer trajectories, boosting diagnostic accuracy by 1-2 orders of magnitude! #MachineLearning #OptimizerDevelopment
Full Article
Title: Gradient-Direction Sensitivity Reveals Linear-Centroid Coupling Hidden by Optimizer Trajectories
Abstract:
arXiv:2604.25143v1 Announce Type: cross Abstract: We show that replacing the rolling SVD of AdamW updates with a rolling SVD of loss gradients changes the diagnostic by 1-2 orders of magnitude. Performing SVD on the loss gradient instead of the AdamW update increases the measured perturbative coupling between SED directions and Linear Centroid Hypothesis (LCH) features from $ \bar{R}_k \approx 3 $--$9\times$ to $100$--$330\times$ across four single-task modular arithmetic operations, eliminating
Abstract:
arXiv:2604.25143v1 Announce Type: cross Abstract: We show that replacing the rolling SVD of AdamW updates with a rolling SVD of loss gradients changes the diagnostic by 1-2 orders of magnitude. Performing SVD on the loss gradient instead of the AdamW update increases the measured perturbative coupling between SED directions and Linear Centroid Hypothesis (LCH) features from $ \bar{R}_k \approx 3 $--$9\times$ to $100$--$330\times$ across four single-task modular arithmetic operations, eliminating
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