Summary of On the Limitations Of Fractal Dimension As a Measure Of Generalization, by Charlie B. Tan et al.
On the Limitations of Fractal Dimension as a Measure of Generalization
by Charlie B. Tan, Inés García-Redondo, Qiquan Wang, Michael M. Bronstein, Anthea Monod
First submitted to arxiv on: 4 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Dynamical Systems (math.DS); 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 research paper explores the generalization gap of overparameterized neural networks, focusing on the framework of fractals to model optimization trajectories. The study evaluates persistent homology-based generalization measures, revealing confounding effects due to hyperparameter variation. Additionally, it observes that fractal dimension fails to predict generalization from poor initializations and identifies double descent in topological generalization measures. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper looks at how well neural networks generalize to new data after being trained on a small amount of data. The researchers use a mathematical concept called fractals to understand why some networks do better than others. They found that the way they measured this didn’t quite match up with how well the network actually generalized, and that different starting points for training made things even more complicated. This study helps us understand what’s going on behind the scenes when neural networks are trained. |
Keywords
» Artificial intelligence » Generalization » Hyperparameter » Optimization
