Summary of Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks, by Hristo Papazov et al.
Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks
by Hristo Papazov, Scott Pesme, Nicolas Flammarion
First submitted to arxiv on: 8 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); 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 investigates the impact of momentum on the optimization trajectory of gradient descent. It proposes a continuous-time approach that helps identify an intrinsic quantity λ that defines the optimization path and provides a simple acceleration rule. The researchers show that small values of λ help recover sparse solutions in an overparametrised regression setting, while providing similar but weaker results for stochastic momentum gradient descent. They also provide numerical experiments to support their claims. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores how using “momentum” in machine learning can affect the way algorithms find the best solution. It shows that a special number called λ can help make sure these algorithms work well and produce simple solutions. The researchers tested this idea on a specific type of neural network and found that small values of λ helped them recover the correct answer more easily. |
Keywords
* Artificial intelligence * Gradient descent * Machine learning * Neural network * Optimization * Regression
