Summary of Curvature-informed Sgd Via General Purpose Lie-group Preconditioners, by Omead Pooladzandi and Xi-lin Li
Curvature-Informed SGD via General Purpose Lie-Group Preconditioners
by Omead Pooladzandi, Xi-Lin Li
First submitted to arxiv on: 7 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed approach accelerates stochastic gradient descent (SGD) by utilizing curvature information from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. The method involves two online-updated preconditioners: a matrix-free one and a low-rank approximation one. These preconditioners are constrained to certain connected Lie groups to preserve symmetry or invariance, simplifying the fitting process and eliminating the need for damping. As a result, the learning rate and step size are naturally normalized, with default values that work well in most scenarios. The approach offers a promising direction for improving SGD convergence with low computational overhead. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper presents a new way to make a popular machine learning algorithm called stochastic gradient descent (SGD) work better and faster. It uses information about the shape of the data, like the BFGS algorithm does, but in a more efficient way that doesn’t require as much computation or tweaking. The approach involves updating two special types of filters that help SGD find the best solution more quickly. These filters are designed to work well with different types of data and don’t need fine-tuning or special handling. As a result, the algorithm can be used on a wide range of problems without needing a lot of extra setup. |
Keywords
* Artificial intelligence * Fine tuning * Machine learning * Stochastic gradient descent
