Supplementary information 1 Simulation parameters

All simulations were based on pytorch [5]. For the nonlinear neuroscience tasks, we applied the gradient descent method "Adam" [4] to the recurrent weights W as well as to the input and output vectors mi, wi. We checked that our results did not depend qualitatively on the choice of the "Adam" algorithm over plain gradient descent; however, training converged more easily for this choice of algorithm. We also checked that restricting training to W only (as for the simple model) did not alter our results qualitatively (although, with this restriction, training on the Romo task for small values of g did not converge). Code for reproducing our results can be found on https://github.com/frschu/neurips_