Low-dimensional dynamical neural population models with shared stimulus drive

Modern experimental technologies enable simultaneous recording of large neural populations. These high-dimensional data present a challenge for analysis. Recent work has focused on extracting low-dimensional dynamical trajectories that may underlie such responses. These methods enable visualization and may also provide insight into neural compuations. However, previous work focused on modeling a population’s dynamics without conditioning on external stimuli. We propose a new technique that integrates linear dimensionality reduction (analogous to the STA and STC) with a latent dynamical system model of neural activity. Under our model, the spike response of a neural population is governed by a low- dimensional dynamical system with quadratic input. In this framework, the number of parameters grows linearly with population (size given fixed latent dimensionality). Hence, it is computationally fast for large populations, unlike fully-connected models. Our method captures both noise correlations and low-dimensional stimulus selectivity through the simultaneous modeling of dynamics and stimulus dependence. This approach is particularly well-suited for studying the population activity of sensory cortices, where neurons often have substantial receptive field overlap