Summary of Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces, by Lei Shi and Jia-qi Yang
Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces
by Lei Shi, Jia-Qi Yang
First submitted to arxiv on: 7 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Functional Analysis (math.FA); Statistics Theory (math.ST)
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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 paper investigates how stochastic gradient descent (SGD) can be used to learn operators between complex mathematical spaces. The authors propose new conditions that describe the structure and complexity of these operators, which helps them understand when SGD will work well or not. They also analyze the convergence rate of SGD and show that it can still work for learning nonlinear operators. Additionally, they apply their analysis to new types of mathematical spaces, refining previous results. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about using a machine learning algorithm called stochastic gradient descent (SGD) to learn how certain math operations work. The authors come up with some rules to help them understand what makes these operations easy or hard for SGD to figure out. They also show that SGD can still be useful even when it’s trying to learn more complicated things. It’s all about understanding when and how this algorithm works best. |
Keywords
* Artificial intelligence * Machine learning * Stochastic gradient descent
