Summary of A Precise Characterization Of Sgd Stability Using Loss Surface Geometry, by Gregory Dexter et al.
A Precise Characterization of SGD Stability Using Loss Surface Geometry
by Gregory Dexter, Borja Ocejo, Sathiya Keerthi, Aman Gupta, Ayan Acharya, Rajiv Khanna
First submitted to arxiv on: 22 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 investigates the optimization algorithm Stochastic Gradient Descent (SGD), which has been empirically successful in various applications. While its practical efficacy is well-documented, theoretical understanding of SGD’s implicit regularization remains limited. The authors build upon previous research that linked linear stability to sharpness and generalization error in overparameterized neural networks. They introduce a novel coherence measure for the loss Hessian, enabling them to provide simplified sufficient conditions for identifying linear instability at an optimum. This work extends existing analyses by relaxing assumptions and applying to a broader range of loss functions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary SGD is an important tool used to train models, but scientists don’t fully understand why it works so well. Researchers have found that a key factor in SGD’s success is its ability to make the optimization problem harder or easier depending on the data. This paper digs deeper into this relationship and provides new ways to identify when SGD might not work as well. By introducing a new measure of how the loss changes, scientists can now better predict when SGD will struggle. |
Keywords
* Artificial intelligence * Generalization * Optimization * Regularization * Stochastic gradient descent
