Summary of Is All Learning (natural) Gradient Descent?, by Lucas Shoji et al.
Is All Learning (Natural) Gradient Descent?
by Lucas Shoji, Kenta Suzuki, Leo Kozachkov
First submitted to arxiv on: 24 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Dynamical Systems (math.DS); Neurons and Cognition (q-bio.NC)
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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 A wide class of effective learning rules can be rewritten as natural gradient descent with respect to a suitably defined loss function and metric. Specifically, we show that parameter updates within this class of learning rules can be expressed as the product of a symmetric positive definite matrix (i.e., a metric) and the negative gradient of a loss function. We also demonstrate that these metrics have a canonical form and identify several optimal ones, including the metric that achieves the minimum possible condition number. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows how some learning rules can be rewritten as natural gradient descent with respect to a defined loss function and metric. It proves that this class of learning rules can be expressed using a special matrix (metric) and the negative gradient of a loss function. The proof is simple, relying only on basic math concepts. |
Keywords
» Artificial intelligence » Gradient descent » Loss function
