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Abstract

Modern experimental technologies such as multi-electrode arrays and 2-photon population calcium imaging make it possible to record the responses of large neural populations (up to 100s of neurons) simultaneously. These high-dimensional data pose a significant challenge for analysis. Recent work has focused on extracting lowdimensional dynamical trajectories that may underlie such responses. These methods enable visualization of high-dimensional neural activity, and may also provide insight into the function of underlying circuitry. Previous work, however, has primarily focused on models of a opulation’s intrinsic dynamics, without taking into account any external stimulus drive. We propose a new technique that integrates linear dimensionality reduction of stimulus-response functions (analogous to spike-triggered average and covariance analysis) with a latent dynamical system (LDS) model of neural activity. Under our model, the population response is governed by a low-dimensional dynamical system with nonlinear (quadratic) stimulus-dependent input. Parameters of the model can be learned by combining standard expectation maximization for linear dynamical system models with a recently proposed algorithms for learning quadratic feature selectivity. Unlike models with all-to-all connectivity, this framework scales well to large populations since, given fixed latent dimensionality, the number of parameters grows linearly with population size. Simultaneous modeling of dynamics and stimulus dependence allows our method to model correlations in response variability while also uncovering low-dimensional stimulus selectivity that is shared across a population. Because stimulus selectivity and noise correlations both arise from coupling to the underlying dynamical system, it is particularly well-suited for studying the neural population activity of sensory cortices, where stimulus inputs received by different neurons are likely to be mediated by local circuitry, giving rise to both shared dynamics and substantial receptive field overlap.