Summary of Linear Recursive Feature Machines Provably Recover Low-rank Matrices, by Adityanarayanan Radhakrishnan et al.
Linear Recursive Feature Machines provably recover low-rank matrices
by Adityanarayanan Radhakrishnan, Mikhail Belkin, Dmitriy Drusvyatskiy
First submitted to arxiv on: 9 Jan 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 proposed Recursive Feature Machines (RFMs) are a novel algorithm that explicitly performs feature learning by alternating between reweighting feature vectors and learning prediction functions in the transformed space. By analyzing the class of overparametrized problems in sparse linear regression and low-rank matrix recovery, this paper provides theoretical guarantees for how RFM performs dimensionality reduction. The authors show that restricted RFM (lin-RFM) generalizes the well-studied Iteratively Reweighted Least Squares (IRLS) algorithm. Additionally, they provide an implementation of lin-RFM that outperforms deep linear networks in sparse linear regression and low-rank matrix completion. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper studies how neural networks make predictions by looking at something called feature learning. Feature learning is like a shortcut that helps neural networks work well even when dealing with lots of data. The authors created an algorithm called Recursive Feature Machines (RFMs) that does this feature learning in a special way. They tested RFM on some important problems and found it works really well, especially when there are missing pieces of information. This is useful because it means we can use RFM to solve real-world problems faster and better. |
Keywords
* Artificial intelligence * Dimensionality reduction * Linear regression
