Summary of Learnability Of High-dimensional Targets by Two-parameter Models and Gradient Flow, By Dmitry Yarotsky
Learnability of high-dimensional targets by two-parameter models and gradient flow
by Dmitry Yarotsky
First submitted to arxiv on: 26 Feb 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 The research paper investigates the theoretical limitations of learning high-dimensional targets using W-parameter models and gradient flow (GF) when W<d. The main result shows that certain probability distributions can be learned with arbitrary success probability using models with as few as two parameters. However, for W<d, there is a large subset of non-learnable targets. The study also highlights the limitations of hierarchical procedures in achieving learnability and demonstrates that most elementary function-based models cannot achieve the level of learnability demonstrated. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In simple terms, this paper explores how well we can understand complex data sets using different types of mathematical models. It shows that with certain kinds of probability distributions, it’s possible to learn about these data sets with very high accuracy using surprisingly simple models. However, for more complex data sets, there are limits to what we can learn. The study also reveals a surprising fact: many ways of combining simple building blocks (like elementary functions) cannot be used to learn certain types of data. |
Keywords
* Artificial intelligence * Probability
