Summary of Deep Neural Networks Are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation, by Hao Liu et al.
Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation
by Hao Liu, Jiahui Cheng, Wenjing Liao
First submitted to arxiv on: 8 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 Deep learning has achieved impressive outcomes across various fields, prompting researchers to investigate its theoretical foundations. This paper takes a different approach by examining how deep neural networks adapt to diverse regularity in functions across locations, scales, and non-uniform data distributions. Specifically, it focuses on a broad class of functions defined by nonlinear tree-based approximation, encompassing uniform and discontinuous functions. The authors develop non-parametric approximation and estimation theories using deep ReLU networks, showing that these models are adaptive to different regularity and non-uniform data distributions. Numerical experiments validate the results, which have implications for various function classes. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Deep learning is a powerful tool that has achieved great things in many areas. But how does it actually work? This paper looks at something called “nonlinear tree-based approximation” and shows how deep neural networks can adapt to different patterns in data. It’s like trying to draw a picture with different brushes and colors, depending on what you’re drawing. The results are very promising and could be used in many different areas. |
Keywords
» Artificial intelligence » Deep learning » Prompting » Relu
