Summary of Can Stability Be Detrimental? Better Generalization Through Gradient Descent Instabilities, by Lawrence Wang et al.
Can Stability be Detrimental? Better Generalization through Gradient Descent Instabilities
by Lawrence Wang, Stephen J. Roberts
First submitted to arxiv on: 23 Dec 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the relationship between gradient descent optimization, sharpness, and deep neural networks. Traditional analyses suggest that stable training is achieved when the largest eigenvalue of the loss Hessian (sharpness) is below a critical learning-rate threshold. However, recent studies indicate that modern deep neural networks can achieve good performance despite operating outside this regime. The authors demonstrate that instabilities induced by large learning rates move model parameters toward flatter regions of the loss landscape, which allows for exploration of more desirable geometrical properties for generalization, such as flatness. They prove that network depth causes unstable growth in parameters to rotate the principal components of the Hessian, promoting exploration of the parameter space away from unstable directions. Empirical studies reveal an implicit regularization effect in gradient descent with large learning rates operating beyond the stability threshold, leading to excellent generalization performance on modern benchmark datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how deep neural networks work and why they’re good at predicting things. Normally, we think that when a network is “stable” it does well, but some studies say this isn’t true. The researchers found that when a network gets a little unstable, its parameters move to a flatter place in the loss landscape, which helps it do better on new data. This happens because the depth of the network makes the parameters move around and change direction, allowing the network to explore more useful areas. |
Keywords
» Artificial intelligence » Generalization » Gradient descent » Optimization » Regularization
