Simultaneous recordings of many neurons embedded within a recurrently-connected cortical network may provide concurrent views into the dynamical processes of that network, and thus its computational function. In principle, these dynamics might be identified by purely unsupervised, statistical means. Here, we show that a Hidden Switching Linear Dynamical Systems (HSLDS) model---in which multiple linear dynamical laws approximate a nonlinear and potentially non-stationary dynamical process---is able to distinguish different dynamical regimes within single-trial motor cortical activity associated with the preparation and initiation of hand movements. The regimes are identified without reference to behavioural or experimental epochs, but nonetheless transitions between them correlate strongly with external events whose timing may vary from trial to trial. The HSLDS model also performs better than recent comparable models in predicting the firing rate of an isolated neuron based on the firing rates of others, suggesting that it captures more of the "shared variance" of the data. Thus, the method is able to trace the dynamical processes underlying the coordinated evolution of network activity in a way that appears to reflect its computational role.

Increasing the performance of neural prostheses is necessary for assuring their clinical viability. One performance limitation is the presence of correlated trial-to-trial variability that can cause neural responses to wax and wane in concert as the subject is, for example, more attentive or more fatigued. We report here the design and characterization of a Factor- Analysis-based decoding algorithm that is able to contend with this confound. We characterize the decoder (classifier) on a previously reported dataset where monkeys performed both a real reach task and a prosthetic cursor movement task while we recorded from 96 electrodes implanted in dorsal pre- motor cortex. In principle, the decoder infers the underlying factors that co-modulate the neurons' responses and can use this information to function with reduced error rates (1 of 8 reach target prediction) of up to ~75% (~20% total prediction error using independent Gaussian or Poisson models became ~5%). Such Factor-Analysis based methods appear to be effective when attempting to combat directly unobserved trial-by-trial neural variabiliy.

We consider the problem of extracting smooth low-dimensional neural trajectories'' that summarize the activity recorded simultaneously from tens to hundreds of neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional noisy spiking activity in a compact denoised form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the data are firstdenoised'' by smoothing over time, then a static dimensionality reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way, and account for spiking variability that may vary both across neurons and across time. We then present a novel method for extracting neural trajectories, Gaussian-process factor analysis (GPFA), which unifies the smoothing and dimensionality reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that GPFA provided a better characterization of the population activity than the two-stage methods. From the extracted single-trial neural trajectories, we directly observed a convergence in neural state during motor planning, an effect suggestive of attractor dynamics that was shown indirectly by previous studies.

Spiking activity from neurophysiological experiments often exhibits dy- namics beyond that driven by external stimulation, presumably reflect- ing the extensive recurrence of neural circuitry. Characterizing these dynamics may reveal important features of neural computation, par- ticularly during internally-driven cognitive operations. For example, the activity of premotor cortex (PMd) neurons during an instructed de- lay period separating movement-target specification and a movement- initiation cue is believed to be involved in motor planning. We show that the dynamics underlying this activity can be captured by a low- dimensional non-linear dynamical systems model, with underlying re- current structure and stochastic point-process output. We present and validate latent variable methods that simultaneously estimate the system parameters and the trial-by-trial dynamical trajectories. These meth- ods are applied to characterize the dynamics in PMd data recorded from a chronically-implanted 96-electrode array while monkeys perform delayed-reach tasks.