In neuroscience we often ask which dynamical system model generated the data? However, our ability to distinguish between dynamical hypotheses from data is hindered by model non-identifiability. For example, the two systems below are indistinguishable using observational data (1/n).

Can we use interventional data to identify the dynamics? Intuitively, interventions kick the state of the system outside of its attractor manifold, allowing for the exploration of the state space (Jazayeri et al 2017) (2/n).

We propose interventional state space models (iSSM), a statistical framework for the joint modeling of observational and interventional data. Compared to SSM, iSSM models interventions in a causal manner, where the interventions decouple nodes from their causal parents (3/n).

Under some assumptions (bounded completeness of the observation noise, injectivity of the mixing function, and faithfulness) we prove that, under sufficiently diverse interventions, iSSM is able to recover the true latents, dynamics, emissions, and noise parameters (4/n).

In models of motor cortex dynamics with linear dynamics and nonlinear observations, we show that iSSM can identify the underlying dynamics and emissions, and recover the true latent variables. The accuracy of this recovery improves when more interventions are applied (5/n).

In the linear models of persistent activity in working memory, we show that iSSM can recover the true connectivity matrix with a high precision. For partial observations, this identification problem was originally posed as an open problem in the literature (Qian et al 2024) (6/n).

We apply iSSM to calcium recordings and photo-stimulation from mice's ALM area during a short-term memory task. We show that the latent variables inferred by the iSSM can distinguish between correct and incorrect trials, showing their behavioral relevance (7/n).

In electrophysiological recordings from the monkey prefrontal cortex during electrical micro-stimulation, we show that iSSM generalizes to unseen test interventions, an important property of identifiable models (8/n).