Venue: ICLR 2023 TinyPapers

Reviews:

final_score: rating: Clear, Correct, and Reproducible (CCR): a submission which meets the reviewing criteria
review_content: summary_of_contributions: The responsibility problem describes an issue when training neural networks with unordered targets: the fixed permutation of output units requires that each assume a responsibility for some elements. Prior work has proved the existence of the issue by identifying a single discontinuity. In this paper, the authors show that discontinuities under such models are uncountably infinite, motivating further research into neural networks for unordered data.
strengths_and_weaknesses: The contribution of the paper is clearly presented, but needs some fixes regarding English and grammatical aspects. In the Appendix are all the necessary demonstrations relative to the theorems and prepositions stated. The article, therefore, turns out to be correct and reproducible from a theoretical point of view.
suggested_changes: It would have been nice to see one experimental result. Finally, the paper could provide information about the limitation of the proposed approach.
review_title: null

final_score: rating: Great Start (GS): a submission which meets some of the reviewing criteria but has room for improvement
review_content: summary_of_contributions: This paper proves that maps which assign set elements to a fixed ordering must be discontinuous. 
strengths_and_weaknesses: I assess the paper's strengths and weaknesses with respect to each of the reviewing criteria below:

- **Clarity**: The text is fairly well-organized, and at a high level its logical structure is easy to understand. 

- **Correctness**: I have not checked the proofs carefully, because I am not familiar with many of the relevant references. 

- **Reproducibility**: To the best of my understanding, adequate details are given in the main text and appendices. 

- **Follows basic requirements**: The paper fits within the two-page limit, and is adequately anonymized. 
suggested_changes: This paper lies far outside my area of expertise, and my assessment of its correctness is therefore an educated guess. I apologize to the author and area chairs for my inability to offer useful comments.
review_title: null

Decision: Invite to archive