Preconditioner on Matrix Lie Group for SGD
We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher information matrix. Both preconditioners can be derived from one framework, and efficiently estimated on any matrix Lie groups designated by the user using natural or relative gradient descent minimizing certain preconditioner estimation criteria. Many existing preconditioners and methods, e.g., RMSProp, Adam, KFAC, equilibrated SGD, batch normalization, etc., are special cases of or closely related to either the Newton type or the Fisher type ones. Experimental results on relatively large scale machine learning problems are reported for performance study.
 The authors suggest and analyse two types of preconditioners for optimization, a Newton type and a Fisher type preconditioner. The paper is well written, the analysis is clear and the significance is arguably given. The authors run their optimizers on a synthetic benchmark data set and on imagenet. The originality is not so high as the this line of research exists for long. The "Lie" in the title is (technically correct, but) a bit misleading, as only matrix groups were used.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Preconditioner on Matrix Lie Group for SGD
We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher information matrix. Both preconditioners can be derived from one framework, and efficiently estimated on any matrix Lie groups designated by the user using natural or relative gradient descent minimizing certain preconditioner estimation criteria. Many existing preconditioners and methods, e.g., RMSProp, Adam, KFAC, equilibrated SGD, batch normalization, etc., are special cases of or closely related to either the Newton type or the Fisher type ones. Experimental results on relatively large scale machine learning problems are reported for performance study.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The authors suggest and analyse two types of preconditioners for optimization, a Newton type and a Fisher type preconditioner. The paper is well written, the analysis is clear and the significance is arguably given. The authors run their optimizers on a synthetic benchmark data set and on imagenet. The originality is not so high as the this line of research exists for long. The "Lie" in the title is (technically correct, but) a bit misleading, as only matrix groups were used.
assistant
 The authors suggest and analyse two types of preconditioners for optimization, a Newton type and a Fisher type preconditioner. The paper is well written, the analysis is clear and the significance is arguably given. The authors run their optimizers on a synthetic benchmark data set and on imagenet. The originality is not so high as the this line of research exists for long. The "Lie" in the title is (technically correct, but) a bit misleading, as only matrix groups were used.