Inferring Multi-Timescale Neural Dynamics with Switching Linear Dynamical Systems

Neural activity often exhibits multiple timescales that can vary with behavioral states and task conditions. Identifying these timescales from neural recordings is important for better understanding neural computation and function. However, traditional approaches based on autocorrelation fitting are difficult to scale to high-dimensional population recordings and can become unreliable when neural dynamics change with behavior. State-space models have been a powerful framework for modeling high-dimensional neural population activity through latent dynamical systems, but standard formulations and inference methods do not explicitly account for multiple timescales and therefore do not guarantee accurate recovery of the underlying temporal structure. Motivated by these questions, we introduce the Multi-Timescale Switching Linear Dynamical System (MTS-SLDS), a framework for identifying regime-specific latent timescales from continuous or spiking neural observations. MTS-SLDS combines a multi-lag moment initialization, which captures temporal structure across multiple observation lags, with regime-conditioned Laplace-EM inference, which reduces mixing of dynamical statistics across uncertain regimes. Characteristic timescales can then be extracted directly from the eigenvalues of the learned latent transition matrices. In synthetic experiments with Gaussian and Poisson observations, MTS-SLDS accurately recovers timescales and switching structure over a range of signal levels. We further apply this framework on neural spike recordings from two behavioral tasks. During a fixation task with neural activity recorded from V4, the inferred timescales agree with estimates from a dedicated Bayesian autocorrelation method. In Area 2 motor cortex recordings during a reaching task, we find that MTS-SLDS identifies behaviorally aligned dynamical regimes and provides more interpretable regime-specific timescale estimates. These results establish MTS-SLDS as a reliable framework for investigating how neural timescales behave within and across behavioral states, and for studying their role in neural population dynamics.