Checklist
The checklist follows the references. Please
read the checklist guidelines carefully for information on how to answer these
questions. For each question, change the default [TODO] to [Yes] , [No] , or [N/A] . You are strongly encouraged to include a justification to your answer , either by referencing the appropriate section of
your paper or providing a brief inline description. For example:

Did you include the license to the code and datasets? [Yes] See Section LABEL:gen_inst .

Did you include the license to the code and datasets? [No] The code and the data are proprietary.

Did you include the license to the code and datasets? [N/A]

Please do not modify the questions and only use the provided macros for your
answers. Note that the Checklist section does not count towards the page
limit. In your paper, please delete this instructions block and only keep the
Checklist section heading above along with the questions/answers below.

For all authors…

Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] To make this easier for the readers, we have referred to the pertinent Figures and Theorem to support our summary of contributions in Introduction.

Did you describe the limitations of your work? [Yes] Limitations and future work can be found in our Discussion section.

Did you discuss any potential negative societal impacts of your work? [No] This work contributes to the theoretical understanding of biologically-plausible learning rules for recurrent neural networks. As such, we do not anticipate any direct ethical or societal impact. In the long-term, our work can have impact on related research communities such as neuroscience and deep learning, with societal impact depending on the development of these fields.

Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We have carefully read the ethics review guidelines and confirm that this
paper conforms to them.

If you are including theoretical results…

Did you state the full set of assumptions of all theoretical results? [Yes] We state all assumptions precisely when we first presented the Theorem in Results, We further details, discussions and proofs in the appendix.

Did you include complete proofs of all theoretical results? [Yes] Proofs can be found in Appendix B .

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] Anonymized code link is provided in Appendix A.3 .

Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] All training details are provided in Appendix A.3 .

Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We tried to provide this information in all applicable figures. This is stated as "Solid lines/shaded regions: mean/standard deviation obtained at the end of training across five independent runs" in the legends of several figures.

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] Information pertaining to computing resources and simulation time can be found in Appendix A.3 .

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] For dataset, we cited MNIST as well as representative neuroscience papers for the two neuroscience motivated tasks. We have also cited existing coding assets in Appendix A.3 .

Did you mention the license of the assets? [Yes] We mentioned that in Appendix A.3 .

Did you include any new assets either in the supplemental material or as a URL? [No]

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]