Summary of Bounds For the Smallest Eigenvalue Of the Ntk For Arbitrary Spherical Data Of Arbitrary Dimension, by Kedar Karhadkar et al.
Bounds for the smallest eigenvalue of the NTK for arbitrary spherical data of arbitrary dimension
by Kedar Karhadkar, Michael Murray, Guido Montúfar
First submitted to arxiv on: 23 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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 This paper focuses on establishing bounds for the smallest eigenvalue of the neural tangent kernel (NTK), a crucial component in analyzing neural network optimization and memorization. Existing approaches rely on distributional assumptions about the data and are limited to high-dimensional settings where input dimension d0 scales logarithmically with the number of samples n. This work breaks new ground by providing bounds without these requirements, instead leveraging a measure of collinearity in the data. The results hold with high probability even when d0 is held constant versus n. The authors achieve this through a novel application of the hemisphere transform. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper explores how neural networks learn and remember new information. Right now, it’s hard to predict how well these networks will do without making certain assumptions about the data they’re trained on. But the team behind this study wants to change that. They’ve developed a way to understand neural networks better by looking at the smallest eigenvalue of something called the neural tangent kernel (NTK). This new approach doesn’t need those assumptions and works even when there are only a few inputs versus many examples. The team used a special technique called the hemisphere transform to make it all work. |
Keywords
» Artificial intelligence » Neural network » Optimization » Probability
