Stochastic activity in low-rank recurrent neural networks
Fig 3
Rank-one RNN receiving high-dimensional stochastic inputs.
A. Model architecture. B. The activity covariance is high-dimensional, with all eigenvalues taking identical values except for two – one larger and one smaller. The principal components associated with these two eigenvalues lie within the plane spanned by the connectivity vectors m and n. C. Covariance eigenvalues as a function of overlap between connectivity vectors. The dashed vertical line indicates the value of for which dynamics become unstable. Black arrows indicate the value of
that is used for simulations in Fig 4. D. Dimensionality. Horizontal black lines indicate the maximum (N) and the minimum (1) possible values. E. Components of
(or PC1 vector, left) and
(or PCN vector, right) along connectivity vectors m and n, as from Eq 24. F. Overlap (Eq 4) between the principal components
and
(after normalization) and the connectivity vectors m and n.