Summary of Depth Separation in Norm-bounded Infinite-width Neural Networks, by Suzanna Parkinson et al.
Depth Separation in Norm-Bounded Infinite-Width Neural Networks
by Suzanna Parkinson, Greg Ongie, Rebecca Willett, Ohad Shamir, Nathan Srebro
First submitted to arxiv on: 13 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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 research explores depth separation in infinite-width neural networks, focusing on the control of complexity through the overall squared L2-norm of weights. The study shows that there are functions that can be learned with polynomial sample complexity using depth-3 ReLU networks, but not with sub-exponential sample complexity using depth-2 ReLU networks, regardless of the norm value. Conversely, any function learnable with polynomial sample complexity by a depth-2 ReLU network is also learnable with polynomial sample complexity by a depth-3 ReLU network. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study looks at how deep neural networks can learn and generalize well. It shows that some functions are easy to learn with a certain type of network, but not as easy with another type, even if the network gets really wide. The researchers also found that any function that’s easy to learn with one type of network is also easy to learn with another type. |
Keywords
* Artificial intelligence * Relu
