Fig. 2: Multiscale dynamical modeling and modal analysis.

a We first learn the dynamical model from the neural activity in the training set. The neural activity can be in the form of spiking, LFP, or combined spike-LFP activity. b After learning the dynamical model, we find the principal modes that characterize neural dynamics. Each principal mode has a unique pair of dynamical characteristics consisting of a decay and frequency and indicating how fast one component of neural response decays in time and with what frequency it rings over time in response to excitations. c To get the principal modes, for the same neural activity, we learn dynamical models of various latent state dimensions. For each dimension, we indicate the location of the modes corresponding to their real and imaginary values on a plane parallel to the x–y plane and intersecting the z axis at that dimension. We finally cluster the modes using K-means clustering to find the vertical clusters, each corresponding to a different location on the x–y plane and thus different decay-frequency characteristics. d In the test set, we use the learned dynamical model to estimate the modes and states. We then use the estimated state to predict behavior and predict neural activity one-step-ahead into the future, and we separate the contribution of each mode in these predictions. By comparing the contribution of each mode with true behavior and neural activity, we get each modes’ behavior prediction accuracy and one-step-ahead prediction accuracy of neural activity. This accuracy is quantified with correlation coefficient (CC) for behavior and LFP features and with prediction power (PP) for spike events (Methods).