Summary of On the Crucial Role Of Initialization For Matrix Factorization, by Bingcong Li et al.
On the Crucial Role of Initialization for Matrix Factorization
by Bingcong Li, Liang Zhang, Aryan Mokhtari, Niao He
First submitted to arxiv on: 24 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Signal Processing (eess.SP); Optimization and Control (math.OC)
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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 revisits the classic low-rank matrix factorization problem and highlights the crucial role of initialization in determining convergence rates for non-convex and non-smooth optimization. The authors introduce Nystrom initialization, which significantly improves the global convergence of Scaled Gradient Descent (ScaledGD) in both symmetric and asymmetric matrix factorization tasks. They demonstrate that ScaledGD with Nystrom initialization achieves quadratic convergence in cases where only linear rates were previously known. Furthermore, they extend this initialization to low-rank adapters (LoRA) commonly used for fine-tuning foundation models, resulting in NoRA, which shows superior performance across various downstream tasks and model scales. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how to improve a type of math problem called matrix factorization. It’s like trying to find the best way to represent a complex picture as a combination of simpler pieces. The researchers found that the way they started solving this problem was very important, and they came up with a new technique called Nystrom initialization. This helps make sure the solution is good not just close by, but all the way to the end. They also showed how this works well for bigger models used in things like language translation and image recognition. |
Keywords
» Artificial intelligence » Fine tuning » Gradient descent » Lora » Optimization » Translation
