Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
Fig 10
Links between properties of system dynamics captured by the PLRNN-BOLD-SSM and behavioral task performance.
A. Average power spectra for PLRNN-generated time series when external inputs were excluded (left) and included (right), and for the original BOLD traces (yellow). M = 9 latent states were used in this analysis, as at this M the number of stable and unstable objects appeared to roughly plateau (S2A Fig). The left grey line marks the frequency of one entire task sequence cycle (3⋅72s = 216s = .0046Hz) and the right grey line the frequency of one task and resting block (36s+36s = 72s = .0139 Hz). The peaks in the power spectra of the model-generated time series at these points indicate that the PLRNN has captured the periodic reoccurrence of single task blocks as well as that of the whole task block sequence in its limit cycle activity. B. Relation of the number of stable and unstable dynamical objects (see Methods) to behavioral performance for models without external inputs (M = 9; see S2B Fig for data pooled across M = 2…10). Low and high performance groups were formed according to median splits over correct responses during the CMT. A repeated measures ANOVA with between-subject factor ‘performance’ (‘low’ vs. ‘high’ percentage of correct responses) and within-subject factor ‘stability’ (‘stable’ vs. ‘unstable’ objects) revealed a significant 2-way ‘performance x stability’ interaction (F(1,24) = 5.28, p = .031). We focused on the CMT for this analysis since for the other two tasks performance was close to a ceiling effect (although results still hold when averaging across tasks, p = .012).