Summary of the main results obtained for recurrent neural networks with rank-one connectivity.

In the second column, we report the directions defining the part of the covariance matrix (Eq 11) that originates from recurrent activity. (Note that also input directions contribute, via the term .) In the fourth column, the structure of connectivity vectors determines the precise value taken by dimensionality. For intermediate input dimensionality, covariance spectra have not been formally analyzed. Simulations suggest that, among the C + 1 eigenvalues that do not vanish, are approximately fixed to the reference value, while three depend on connectivity.