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Stochastic activity in low-rank recurrent neural networks

Fig 2

Rank-one RNN receiving one-dimensional stochastic inputs.

A. Model architecture. B. Activity covariance is low-dimensional, and is spanned by connectivity vector m together with the external input vector u. As a consequence, activity is contained within the plane collinear with these two vectors. C–D–E. Example of a simulated network with . In C: covariance spectrum. Components larger than 10 are not displayed (they are all close to zero). In D: overlap between the dominant principal components estimated from simulated activity and the theoretically-estimated PCs (left), or the vectors m and u (right). Overlaps are quantified via Eq 4, with input vectors u chosen to be normalized. Note that here, but not in G, only one principal component can be identified. In E: simulated activity projected on the two dominant PCs. F–G–H. Same as in C–D–E, example with .

doi: https://doi.org/10.1371/journal.pcbi.1013371.g002