Identifying Neural Dynamics Using Interventional State Space Models

Neural circuits produce signals that are complex and nonlinear. To facilitate the understanding of neural dynamics, a popular approach is to fit state space models (SSM) to the data and analyze the dynamics of the low-dimensional latent variables. Despite the power of SSM to explain the dynamics of neural circuits, these models have been shown to merely capture statistical associations in the data and cannot be causally interpreted. Therefore, an important research problem is to build models that can predict neural dynamics under causal manipulations. Here, we propose interventional state-space models (iSSM), a class of causal models that can predict neural responses to novel perturbations. We draw on recent advances in causal dynamical systems and present theoretical results for the identifiability of iSSM. In simulations of the motor cortex, we show that iSSM can recover the true latents and the underlying dynamics. In addition, we illustrate two applications of iSSM in biological datasets. First, we applied iSSM to a dataset of calcium recordings from ALM neurons in mice during photostimulation. Second, we applied iSSM to a dataset of electrophysiological recordings from macaque dlPFC during micro-stimulation. In both cases, we show that iSSM outperforms SSM and results in identifiable parameters. The code is available at https://github.com/amin-nejat/issm.

Understanding how the brain works is complicated because the signals produced by neural circuits are complex and constantly changing. To make sense of this activity, scientists often use mathematical tools called state space models (SSMs), which help simplify and analyze brain signals. However, these models only show patterns in the data — they can’t explain how the brain would respond to changes or interventions.To address this, we developed a new kind of model called the interventional state space model (iSSM). Unlike traditional models, iSSM can predict how the brain will react when it’s actively stimulated or changed, making it useful for understanding cause-and-effect relationships in the brain.We tested this new model using simulations of brain activity in the motor cortex and found it could accurately recover the hidden dynamics behind the signals. We also applied it to two real-world brain datasets: one from mice that were exposed to light stimulation, and another from monkeys that received tiny electric pulses in their brain. In both cases, our model performed better than traditional ones and gave more meaningful, interpretable results.