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Reviewer 4: The authors may want to devote more attention to introducing the problem. It would seem to me that the dynamics in this low-dimensional subspace, Eq.(1), should be mediated by neurons and their synaptic connections. However, Eq.(1) does not include the synaptic connectivity matrix D, which instead appears in Eq.2. Because the authors point out that the low-dimensional dynamics would be present even in the absence of inputs (u_t 0) I don't understand what physical substrate underlies the dynamics of low-dimensional activity. There are many theoretical and experimental results supporting the existence of low-dimensional dynamics in some neural systems.