Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 6: Weak Accept
review_content: 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.

review_title: Official Blind Review #2

final_score: rating: 8: Accept
review_content: Contribution
This paper proposes algorithm for transferring knowledge from easy -to-solved to complex tasks or from already solve to new tasks. It relies on homotopy functions and sequentially solves a sequence of optimization problems where the task distribution is gradually deformed from a source task to the target task. Theoretical guarantees are provided and proven in a strongly convex setting. The main results from the theory show that the distance between the final solution and its optimal are less or equal to  relative to the distance of the initial source solution to its optimum. So a near optimal solution for the source task will lead to near optimal solution for the target task. Regression and Classification experimentations show competitive results compared to  random and warm-start initialization schemes.

Clarity
Overall, the paper is well written, well motivated and well structured. The technical content is also very clear and excellent.
 Minor point: Seems that there is a notation error in proposition G.1 and its proof (i instead of i+1).


Novelty
The novelty in this work seems to be the application of homotopy methods to the transfer learning settings. The mathematical guarantees are also new and may even offer new ways to interpret fine tuning methods that have been so successful in recent literature. 

However, given the  non-convexity of DNNs, it seems like the analysis in the non-convex settings and its implications  should be part of the main text.

Experiments:
Overall, the experiments are very insightful but limited since you only show the training loss and the validation performance is not evaluated at all. Other things that would could be  beneficial in better assessing the quality of your method are: comparison to Curriculum learning methods, more in depth analysis of the impact of k, and gamma in both regression and classification settings, and solving  toy convex optimization problems to bridge the gap between theory and application.


Preliminary rating:
* Accept *
review_title: Official Blind Review #3

final_score: rating: 3: Weak Reject
review_content: 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.
review_title: Official Blind Review #1

Meta-review: This paper presents a theoretically motivated method based on homotopy continuation for transfer learning and demonstrates encouraging results on FashionMNIST and CIFAR-10. The authors draw a connection between this approach and the widely used fine-tuning heuristic. Reviewers find principled approaches to transfer learning in deep neural networks an important direction, and find the contributions of this paper an encouraging step in that direction. Alongside with the reviewers, I think homotopy continuation is a great numerical tool with a lot of untapped potentials for ML applications, and I am happy to see an instantiation of this approach for transfer learning. Reviewers had some concerns about experimental evaluations (reporting test performance in addition to training), and the writing of the draft. The authors addressed these in the revised version by including test performance in the appendix and rewriting the first parts of the paper. Two out of three reviewers recommend accept. I also find the homotopy analysis interesting and alongside with majority of reviewers, recommend accept. However, please try to iterate at least once more over the writing; simply long sentences and make sure the writing and flow are, for the camera ready version.
Decision: Accept (Poster)