Transferring Optimality Across Data Distributions via Homotopy Methods
Homotopy methods, also known as continuation methods, are a powerful mathematical tool to efficiently solve various problems in numerical analysis, including complex non-convex optimization problems where no or only little prior knowledge regarding the localization of the solutions is available. In this work, we propose a novel homotopy-based numerical method that can be used to transfer knowledge regarding the localization of an optimum across different task distributions in deep learning applications. We validate the proposed methodology with some empirical evaluations in the regression and classification scenarios, where it shows that superior numerical performance can be achieved in popular deep learning benchmarks, i.e. FashionMNIST, CIFAR-10, and draw connections with the widely used fine-tuning heuristic. In addition, we give more insights on the properties of a general homotopy method when used in combination with Stochastic Gradient Descent by conducting a theoretical analysis in a simplified setting.
Authors propose a very general framework of Homotopy to the deep learning set up and explores a few relevant theoretical issues. Though the proposed idea is interesting, the depth and breadth of authors* presentation are simply lacking. The entire paper lacks focus and I suggest authors consider focusing on 1-2 well thought-out ideas. There are many 3-4 line long sentences that are hard to decipher. Please also consider making the presentation more accessible. Overall, this paper does not meet the bar for ICLR.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Transferring Optimality Across Data Distributions via Homotopy Methods
Homotopy methods, also known as continuation methods, are a powerful mathematical tool to efficiently solve various problems in numerical analysis, including complex non-convex optimization problems where no or only little prior knowledge regarding the localization of the solutions is available. In this work, we propose a novel homotopy-based numerical method that can be used to transfer knowledge regarding the localization of an optimum across different task distributions in deep learning applications. We validate the proposed methodology with some empirical evaluations in the regression and classification scenarios, where it shows that superior numerical performance can be achieved in popular deep learning benchmarks, i.e. FashionMNIST, CIFAR-10, and draw connections with the widely used fine-tuning heuristic. In addition, we give more insights on the properties of a general homotopy method when used in combination with Stochastic Gradient Descent by conducting a theoretical analysis in a simplified setting.
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>



Authors propose a very general framework of Homotopy to the deep learning set up and explores a few relevant theoretical issues. Though the proposed idea is interesting, the depth and breadth of authors* presentation are simply lacking. The entire paper lacks focus and I suggest authors consider focusing on 1-2 well thought-out ideas. There are many 3-4 line long sentences that are hard to decipher. Please also consider making the presentation more accessible. Overall, this paper does not meet the bar for ICLR.
assistant
Authors propose a very general framework of Homotopy to the deep learning set up and explores a few relevant theoretical issues. Though the proposed idea is interesting, the depth and breadth of authors* presentation are simply lacking. The entire paper lacks focus and I suggest authors consider focusing on 1-2 well thought-out ideas. There are many 3-4 line long sentences that are hard to decipher. Please also consider making the presentation more accessible. Overall, this paper does not meet the bar for ICLR.