It is well established that temporal organization is critical to memory, and that the ability to temporally organize information is fundamental to many perceptual, cognitive, and motor processes. While our understanding of how the brain processes the spatial context of memories has advanced considerably, our understanding of their temporal organization lags far behind. In this paper, we propose a new approach for elucidating the neural basis of complex behaviors and temporal organization of memories. More specifically, we focus on neural decoding - the prediction of behavioral or experimental conditions based on observed neural data. In general, this is a challenging classification problem, which is of immense interest in neuroscience. Our goal is to develop a new framework that not only improves the overall accuracy of decoding, but also provides a clear latent representation of the decoding process. To accomplish this, our approach uses a Variational Auto-encoder (VAE) model with a diversity-encouraging prior based on determinantal point processes (DPP) to improve latent representation learning by avoiding redundancy in the latent space. We apply our method to data collected from a novel rat experiment that involves presenting repeated sequences of odors at a single port and testing the rats' ability to identify each odor. We show that our method leads to substantially higher accuracy rate for neural decoding and allows to discover novel biological phenomena by providing a clear latent representation of the decoding process.

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data to validate the proposed method.

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of connectivity dynamics. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation.

The hippocampus is critical to the temporal organization of our experiences. Although this fundamental capacity is conserved across modalities and species, its underlying neuronal mechanisms remain unclear. Here we recorded hippocampal activity as rats remembered an extended sequence of nonspatial events unfolding over several seconds, as in daily life episodes in humans. We then developed statistical machine learning methods to analyze the ensemble activity and discovered forms of sequential organization and coding important for order memory judgments. Specifically, we found that hippocampal ensembles provide significant temporal coding throughout nonspatial event sequences, differentiate distinct types of task-critical information sequentially within events, and exhibit theta-associated reactivation of the sequential relationships among events. We also demonstrate that nonspatial event representations are sequentially organized within individual theta cycles and precess across successive cycles. These findings suggest a fundamental function of the hippocampal network is to encode, preserve, and predict the sequential order of experiences.