We would like to thank the entire review team for their efforts and insightful comments. DZPS18] ([DZPS18] refers to arXiv:1810.02054) approach zero (i.e., ImageNet dataset has 14 million images. For those applications, a non-diminishing convergence rate is more desirable. Response to the concern on fixed second layer . Specifically, the same assumption is made in [ADH+19] and [ZCZG18] (arXiv:1811.08888),

We thank the reviewers for their thoughtful comments. An expander graph code allows simple, neurally plausible decoding to perform at par with BP . These expander codes can also be decoded by belief propagation (BP), but it's harder the other way around. We plan to follow this paper with another paper describing neuroscience applications. For space and coherence, this paper focuses on the conceptual theory without elaborating on applications.

We thank all reviewers for their valuable and constructive feedback. We will fix any typos, cite the reference (Durmus et al., 2016), clarify the Revs. We will add more clarification on the class of non-convex potentials at the beginning of the section. Rev. 1 - dimension dependence: Figure on the right shows the asymptotic bias vs To this end, we performed a wall time analysis, whose results were included in App. To summarize the findings, SRK-LD is 2.5-3 times The purpose was to demonstrate that (ii) has a smaller bias than (iii) .

We thank the reviewers for their overall positive feedback. The results are shown in Figure 1. We follow a proof similar to the one given in the original submission.

" the objective function ... is identical to ... DualDICE" -- This assertion

We would like to thank the entire review team for their efforts and insightful comments. DZPS18] ([DZPS18] refers to arXiv:1810.02054) approach zero (i.e., ImageNet dataset has 14 million images. For those applications, a non-diminishing convergence rate is more desirable. Response to the concern on fixed second layer . Specifically, the same assumption is made in [ADH+19] and [ZCZG18] (arXiv:1811.08888),