Summary of Noise Misleads Rotation Invariant Algorithms on Sparse Targets, by Manfred K. Warmuth (1) et al.
Noise misleads rotation invariant algorithms on sparse targets
by Manfred K. Warmuth, Wojciech Kotłowski, Matt Jones, Ehsan Amid
First submitted to arxiv on: 5 Mar 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 This paper explores the limitations of rotation invariant algorithms, particularly in learning sparse linear problems when the number of examples is below the “dimension” of the problem. The study focuses on gradient descent-trained neural networks with fully-connected input layers initialized with rotationally symmetric distributions. The authors show that even for simple sparse problems, such as learning a single feature out of d features, the classification error or regression loss grows with 1-k/n, where k is the number of examples seen. This lower bound becomes vacuous when the number of examples reaches the dimension. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how well certain algorithms do when they’re not very good at recognizing patterns that change direction. These algorithms, called rotation invariant, are used in neural networks and can be initialized with random values that look like circles. The researchers found that even for simple problems where we’re trying to learn one important feature out of many, these algorithms don’t get much better as they see more examples. This is a problem because it means these algorithms won’t be very good at recognizing patterns in real-world data. |
Keywords
* Artificial intelligence * Classification * Gradient descent * Regression
