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.
Based on homotopy,, the paper describes a more rigorous approach to transfer learning than the so called ‘fine-tuning’ heuristic. Progress in the direction of more principled approaches for transfer learning would be tremendously impactful, since one of the core promises of deep learning is the learning of features, which can be used in different downstream tasks. Essentially, (if this reviewer understood this correctly) the idea behind this paper works by interpolation between the original task of interest and a potentially easier to optimize surrogate task. Overall, this reviewer found the concept simple and elegant, and well motivated, and also well introduced. However, since this reviewer does not have a formal background in mathematics, they cannot assess the soundness of the proofs. The paper tests the hypothesis by a simple function approximation regression task, and a classification task to learn to transfer from MNIST to fashion MNIST and MNIST to CIFAR, with promising results. One might argue that a more thorough evaluation would have been desirable, since the claims made by the paper are quite general, and it would have been in the authors’ best interest to present more thorough evidence that their concept works on wider scale of problems, ideally on an NLP task, given the current hype on pre-training with Transformer-based models. Previous work & citations: I would recommend to cite Schmidhuber 1987 (Evolutionary principles in self-referential learning) and Hochreiter et al 2001 (Learning to Learn with gradient descent) in the context of Meta learning. It would be nice to cite Klambauer et al (Self normalizing Networks) in the context of speeding up deep neural network training. The citations of the VGG paper is currently referenced by first names of the authors, not their last names, I am not sure if this was intended.
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>



Based on homotopy,, the paper describes a more rigorous approach to transfer learning than the so called ‘fine-tuning’ heuristic. Progress in the direction of more principled approaches for transfer learning would be tremendously impactful, since one of the core promises of deep learning is the learning of features, which can be used in different downstream tasks. Essentially, (if this reviewer understood this correctly) the idea behind this paper works by interpolation between the original task of interest and a potentially easier to optimize surrogate task. Overall, this reviewer found the concept simple and elegant, and well motivated, and also well introduced. However, since this reviewer does not have a formal background in mathematics, they cannot assess the soundness of the proofs. The paper tests the hypothesis by a simple function approximation regression task, and a classification task to learn to transfer from MNIST to fashion MNIST and MNIST to CIFAR, with promising results. One might argue that a more thorough evaluation would have been desirable, since the claims made by the paper are quite general, and it would have been in the authors’ best interest to present more thorough evidence that their concept works on wider scale of problems, ideally on an NLP task, given the current hype on pre-training with Transformer-based models. Previous work & citations: I would recommend to cite Schmidhuber 1987 (Evolutionary principles in self-referential learning) and Hochreiter et al 2001 (Learning to Learn with gradient descent) in the context of Meta learning. It would be nice to cite Klambauer et al (Self normalizing Networks) in the context of speeding up deep neural network training. The citations of the VGG paper is currently referenced by first names of the authors, not their last names, I am not sure if this was intended.
assistant
Based on homotopy,, the paper describes a more rigorous approach to transfer learning than the so called ‘fine-tuning’ heuristic. Progress in the direction of more principled approaches for transfer learning would be tremendously impactful, since one of the core promises of deep learning is the learning of features, which can be used in different downstream tasks. Essentially, (if this reviewer understood this correctly) the idea behind this paper works by interpolation between the original task of interest and a potentially easier to optimize surrogate task. Overall, this reviewer found the concept simple and elegant, and well motivated, and also well introduced. However, since this reviewer does not have a formal background in mathematics, they cannot assess the soundness of the proofs. The paper tests the hypothesis by a simple function approximation regression task, and a classification task to learn to transfer from MNIST to fashion MNIST and MNIST to CIFAR, with promising results. One might argue that a more thorough evaluation would have been desirable, since the claims made by the paper are quite general, and it would have been in the authors’ best interest to present more thorough evidence that their concept works on wider scale of problems, ideally on an NLP task, given the current hype on pre-training with Transformer-based models. Previous work & citations: I would recommend to cite Schmidhuber 1987 (Evolutionary principles in self-referential learning) and Hochreiter et al 2001 (Learning to Learn with gradient descent) in the context of Meta learning. It would be nice to cite Klambauer et al (Self normalizing Networks) in the context of speeding up deep neural network training. The citations of the VGG paper is currently referenced by first names of the authors, not their last names, I am not sure if this was intended.