Summary of Stochastic Modified Flows For Riemannian Stochastic Gradient Descent, by Benjamin Gess et al.
Stochastic Modified Flows for Riemannian Stochastic Gradient Descent
by Benjamin Gess, Sebastian Kassing, Nimit Rana
First submitted to arxiv on: 2 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Probability (math.PR); 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 Riemannian stochastic gradient descent (RSGD) is a machine learning algorithm that converges to Riemannian gradient flow and a diffusion process called Riemannian stochastic modified flow (RSMF). Researchers used tools from stochastic differential geometry to show that, in the small learning rate regime, RSGD can be approximated by the solution to RSMF driven by an infinite-dimensional Wiener process. The RSMF accounts for random fluctuations of RSGD, increasing the order of approximation compared to deterministic Riemannian gradient flow. The algorithm relies on retraction maps, efficient approximations of exponential maps, and researchers proved quantitative bounds for weak error under assumptions on retraction maps, manifold geometry, and random gradient estimators. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Riemannian stochastic gradient descent is a way computers learn from data that involves complex math. Scientists studied how well this method works by looking at its rate of convergence to two different processes. They found that when the learning rate is small, the algorithm can be approximated by a process called Riemannian stochastic modified flow, which takes into account random fluctuations. This improvement helps the algorithm learn more efficiently. The researchers used special tools from geometry and statistics to prove their findings. |
Keywords
* Artificial intelligence * Diffusion * Machine learning * Stochastic gradient descent
