Summary of Operator Svd with Neural Networks Via Nested Low-rank Approximation, by J. Jon Ryu et al.
Operator SVD with Neural Networks via Nested Low-Rank Approximation
by J. Jon Ryu, Xiangxiang Xu, H. S. Melihcan Erol, Yuheng Bu, Lizhong Zheng, Gregory W. Wornell
First submitted to arxiv on: 6 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Machine Learning (stat.ML)
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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 proposes a new optimization framework for computing eigenvalue decomposition (EVD) of high-dimensional linear operators, using neural networks to parameterize the eigenfunctions. The framework is based on low-rank approximation characterization of truncated singular value decomposition, accompanied by techniques called “nesting” for learning top-L singular values and functions in correct order. This approach promotes orthogonality implicitly and efficiently via unconstrained optimization formulation, making it easy to solve with off-the-shelf gradient-based algorithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a new way to do something important in machine learning and science called eigenvalue decomposition (EVD). It’s like solving a big math problem! Usually, scientists use special computer techniques to solve this problem, but they can be slow or hard to work with. This new approach uses special types of computers called neural networks to help solve the problem. The result is a way to get the right answer fast and easily! |
Keywords
* Artificial intelligence * Machine learning * Optimization
