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1. Introduction
With the advent of large scale intracortical recordings allowing for the simultaneous interrogation of dozens to hundreds of neurons, the study of the role of motor cortex in the generation of movement has been steadily moving toward investigation of cortical dynamics in the brain on the population level. Ensembles of cortical neurons are organized as recurrently connected networks, introducing shared variability among the constituent cells, in turn constraining firing activity to a lower-dimensional space (Yu et al., 2009; Truccolo et al., 2010; Afshar et al., 2011; Churchland et al., 2012; Cunningham and Yu, 2014; Sadtler et al., 2014; Gallego et al., 2017; Pandarinath et al., 2018). Dimensionality reduction techniques can be used to extract the coordinated neural activity of a population, and reveal structures that may be hidden at the isolated single-neuron level. Previous investigations have shown that for reaching movements with the arm, semi-oscillatory dynamics, inferred using jPCA, are a common feature underlying a variety of different reach movements (Churchland et al., 2012). Additionally, a common low-dimensional neural manifold underlying various wrist movements have be found using demixed principle component analysis, or dPCA (Gallego et al., 2018).
Besides dimensionality reduction, many of these techniques also employ dynamical systems models. These models address how the values at the current time step depend on the values at previous time steps, usually in the form of a temporal transition matrix. Poisson Linear-Dynamical-System (PLDS) is one such technique which employs both unsupervised dimensionality reduction as well as explicit temporal dynamics. PLDS maps low-dimensional latent states to the measured high-dimensional neural spiking activity through an observation point-process model and explicitly estimates the dynamics of these latent states as it evolves through time with a linear mapping (Truccolo et al., 2005; Macke et al., 2011). Unlike PCA and dPCA, PLDS models the low-dimensional space as a state-space in a linear dynamical system, thereby explicitly accounting for the temporal relationships in the population. Although these low-dimensional dynamics are inferred through an unsupervised process, they are able to retain relevant behavioral information. In reaching behaviors, explicit state-space models similar to PLDS have been shown to increase closed-loop BMI performance in cursor-control tasks (Kao et al., 2015) and decoding accuracy during forelimb reaching behaviors (Aghagolzadeh and Truccolo, 2014, 2016), demonstrating that...