Summary of How Dnns Break the Curse Of Dimensionality: Compositionality and Symmetry Learning, by Arthur Jacot et al.
How DNNs break the Curse of Dimensionality: Compositionality and Symmetry Learning
by Arthur Jacot, Seok Hoan Choi, Yuxiao Wen
First submitted to arxiv on: 8 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); 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 This paper demonstrates that deep neural networks (DNNs) can efficiently learn complex compositions of functions with bounded F1-norm. The authors derive a generalization bound combining a covering number argument for compositionality and the F1-norm for large width adaptivity. This breakthrough allows DNNs to break the curse of dimensionality, unlike shallow networks. The paper shows that global minimizers of regularized loss can fit compositions of two functions h∘g from limited observations, assuming g is smooth/regular and reduces dimensionality. The authors consider Sobolev norms with different levels of differentiability, well-suited to the F1-norm. Empirical scaling laws reveal phase transitions depending on whether g or h is harder to learn, as predicted by the theory. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows that special kinds of artificial intelligence networks can figure out very complex relationships between things. The authors prove that these networks can do this even when there are many variables involved, which is a big deal because it’s hard for computers to understand relationships in high-dimensional spaces. They also show how these networks can learn from limited data and fit complicated models, like the combination of two functions, by assuming one function simplifies things down and makes them easier to understand. |
Keywords
* Artificial intelligence * Generalization * Scaling laws
