Timescale-Aware Dimensionality Reduction of Neural Dynamics with Predictable Mode Decomposition

Recent methodological advances have enabled high-dimensional recordings of neural activity. These recordings have revealed complex dynamics operating over a hierarchy of interacting timescales. Although several approaches exist to reduce the dimensionality of such datasets, few methods do so while disentangling the dynamics explicitly according to timescales. Inspired by ideas of timescale separation in model reduction of nonlinear dynamical systems, here we present "Predictable Mode Decomposition" (PrMD), a method for reducing dimensionality explicitly by timescale. PrMD reduces high-dimensional data by ordering components based on how far into the future they remain predictable. It finds a linear projection that maximizes the "predictability time" (Tpred)—the integral timescale of the variance explained by a predictive model. For linear-Gaussian dynamics, Tpred is related to the predictive information between past and future. In normal systems (orthonormal eigenvectors) PrMD timescales map to timescales give by the eigenvalues of the dynamics, concentrating predictability along orthogonal modes. While, in non-normal systems, PrMD captures predictive mixtures induced by eigenvector overlap and transient growth. Computationally, PrMD can be solved by a generalized eigenvalue problem, making it easily scalable to large datasets. We demonstrate PrMD on several publicly available neural and behavioral datasets, where it yields dynamically interpretable components that expose a hierarchy of timescales and reveal non-normal structure in the dynamics. PrMD provides a scalable, timescale-aware reduction that ranks neural dynamics by their predictability, identify dynamically coherent motifs and enables construction of simple dynamical systems models of large-scale datasets.