Summary of Benign Overfitting in Fixed Dimension Via Physics-informed Learning with Smooth Inductive Bias, by Honam Wong et al.
Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Bias
by Honam Wong, Wendao Wu, Fanghui Liu, Yiping Lu
First submitted to arxiv on: 13 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Information Theory (cs.IT); Machine Learning (cs.LG); Numerical Analysis (math.NA); Statistics Theory (math.ST)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A machine learning model is developed to reconstruct specific quantities from measurements that comply with certain physical laws, specifically focusing on inverse problems governed by partial differential equations (PDEs). The asymptotic Sobolev norm learning curve for kernel ridge(less) regression is established, showing how the PDE operators can stabilize variance and prevent overfitting in fixed-dimensional problems. The impact of various inductive biases introduced by minimizing different Sobolev norms as a form of implicit regularization is also investigated. For regularized least squares estimators, all considered inductive biases achieve optimal convergence rates when the regularization parameter is chosen correctly. Surprisingly, the smoothness requirement recovered a condition found in Bayesian settings and extends to minimum norm interpolation estimators. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Machine learning can help us reconstruct specific things from measurements that follow certain rules. This paper focuses on solving problems where we know some physical laws. We develop a new way to learn how well our models perform by looking at Sobolev norms, which measure smoothness and roughness. Our results show that the physical laws can actually help our models avoid overfitting (when they become too good at memorizing data). We also find that different ways of regularizing our models can all work well if we choose the right amount of regularization. |
Keywords
* Artificial intelligence * Machine learning * Overfitting * Regression * Regularization
