FIG. 3.
Lyapunov spectra and dimensionality of the gated RNN. (a),(b) The first 50 ordered Lyapunov exponents for a gated RNN (N = 2000) as a function of varying (a) αz and (b) αr. The Lyapunov spectrum is calculated as described in Appendix D. (c) The Kaplan-Yorke dimensionality of the dynamics as a function of αr. (d) The maximal Lyapunov exponent λmax predicted by the DMFT [solving Eqs. (10) and (11); solid line] and obtained numerically using the QR method (circles; N = 2000 and αz = 0). Note that the transition for αr = 20 is sharp; also cf. Fig. 5(c). τz = τt = 2.0 here.