Summary of Stochastic Hessian Fittings with Lie Groups, by Xi-lin Li
Stochastic Hessian Fittings with Lie Groups
by Xi-Lin Li
First submitted to arxiv on: 19 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); 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 A novel approach to stochastic optimization, this paper focuses on the fitting of Hessians or their inverses using a Hessian-fitting criterion from the Preconditioned Stochastic Gradient Descent (PSGD) method. This technique is closely related to second-order and adaptive gradient optimizers such as BFGS, Gaussian-Newton algorithm, natural gradient descent, AdaGrad, etc. The study reveals differences in efficiency and reliability among various preconditioner fitting methods, including closed-form and iterative solutions using Hessian-vector products or stochastic gradients only. The analysis also explores Hessian fittings in Euclidean space, symmetric positive definite (SPL) matrices, and Lie groups. Notably, the paper discovers that Hessian fitting itself is strongly convex under mild conditions in certain general Lie groups, enabling the design of efficient and elegant Lie group sparse preconditioner fitting methods for large-scale stochastic optimizations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at a special way to make computers do mathematical calculations better. It’s called “Hessian” and it helps with things like machine learning and optimization problems. The researchers used a new method to try different ways of fitting the Hessian, which is important because it can help make these calculations faster and more reliable. They found that some methods are better than others, depending on how they’re used. This discovery can be really helpful for making computers do all sorts of tasks, from artificial intelligence to scientific simulations. |
Keywords
* Artificial intelligence * Gradient descent * Machine learning * Optimization * Stochastic gradient descent
