Summary of Stable Minima Cannot Overfit in Univariate Relu Networks: Generalization by Large Step Sizes, By Dan Qiao et al.
Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizes
by Dan Qiao, Kaiqi Zhang, Esha Singh, Daniel Soudry, Yu-Xiang Wang
First submitted to arxiv on: 10 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); 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 generalization capabilities of two-layer ReLU neural networks in univariate nonparametric regression problems with noisy labels. Existing theories are limited due to benign overfitting not occurring, making this problem challenging. The authors introduce a new theory for local minima that gradient descent can stably converge to. They show that gradient descent with a fixed learning rate can only find local minima representing smooth functions with a weighted first-order total variation bounded by 1/- 1/2 + (+ ). The authors also prove a nearly-optimal MSE bound of (n^{-4/5}) within the support of the data points. Extensive simulations demonstrate that large learning rate training induces sparse linear spline fits. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how well neural networks can predict a single value based on some input, even when there’s noise in the data labels. The challenge is that existing theories don’t apply because the problem doesn’t involve overfitting. The authors come up with a new way to understand how gradient descent works in this case, showing it can only find local minima that represent smooth functions. They also prove that neural networks without special regularization techniques can do really well at predicting values. |
Keywords
» Artificial intelligence » Generalization » Gradient descent » Mse » Overfitting » Regression » Regularization » Relu
