Summary of Large Stepsize Gradient Descent For Non-homogeneous Two-layer Networks: Margin Improvement and Fast Optimization, by Yuhang Cai et al.
Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization
by Yuhang Cai, Jingfeng Wu, Song Mei, Michael Lindsey, Peter L. Bartlett
First submitted to arxiv on: 12 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)
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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 investigates the phenomenon of empirical risk oscillations in two-layer neural networks trained using large stepsize gradient descent (GD) under the logistic loss. Researchers show that the second phase begins when the empirical risk falls below a certain threshold, dependent on the stepsize. They also demonstrate an implicit bias of GD in training non-homogeneous predictors, as the normalized margin grows nearly monotonically in the second phase. Additionally, the study reveals that if the dataset is linearly separable and the derivative of the activation function is bounded away from zero, the average empirical risk decreases, implying that the first phase must stop in finite steps. Furthermore, researchers demonstrate that choosing a suitably large stepsize makes GD more efficient than monotonically decreasing the risk. The analysis applies to networks of any width, extending beyond well-known regimes such as the neural tangent kernel and mean-field. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how big neural networks learn. It studies what happens when you train these networks using a certain method called large stepsize gradient descent. Researchers found that there are two phases: one where the network gets worse and one where it gets better. They also showed that the network becomes more biased as it learns, which affects its predictions. Additionally, they discovered that if the data is easy to separate into different groups, the network will learn quickly and stop making mistakes soon. The study found that using a bigger stepsize can make the learning process faster and more efficient. |
Keywords
» Artificial intelligence » Gradient descent
