Checklist
For all authors…

Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] Our main claims in the abstract and introduction accurately reflect the paper’s contributions and scope. In particular, we listed our contributions in Section 1 , and forward referenced each contribution to the corresponding section in the paper.

Did you describe the limitations of your work? [Yes] We clearly defined what is the quantity to measure and what the network is in Section 2 , and what the assumptions are for each theorem in Section 3 .

Did you discuss any potential negative societal impacts of your work? [Yes] We discussed them in Appendix D .

Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We have read the ethics review guidelines. Because our work is to measure the smoothness of neural networks (see Sections 1 and 2 ), and we only used the standard MNIST dataset (see Section 6.1 ), the paper conforms to guidelines.

If you are including theoretical results…

Did you state the full set of assumptions of all theoretical results? [Yes] We clearly defined the quantity to measure and the network structures in Sections 2 , 3 , 4 and 5 .

Did you include complete proofs of all theoretical results? [Yes] We provided important intuition and ideas in the main paper (see Sections 3 , 4 and 5 ), and included complete proofs in Appendix A .

If you ran experiments…

Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] We included the code, data, and instructions as a URL.

Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] We included major experimental setting in Section 6.1 , and detailed specification in Section C.1 .

Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [N/A] Our experiments are deterministic. Given a neural network, our algorithm always returns the same result.

Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] This was provided in Section C.1 .

If you are using existing assets (e.g., code, data, models) or curating/releasing new assets…

If your work uses existing assets, did you cite the creators? [Yes] In terms of dataset, we only used the standard MNIST, and cited the creators. All the tools used in the paper were properly cited. See Sections 6.1 and C.1 .

Did you mention the license of the assets? [Yes] See Section C.1 .

Did you include any new assets either in the supplemental material or as a URL? [Yes] We included our code as a URL.

Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]

Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]

If you used crowdsourcing or conducted research with human subjects…

Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]

Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]

Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]