Further Observations on the Rotational Structure in Neural Data

While the brain obviously performs very sophisticated functions, neurophysiological studies conducted over the last several decades have scrutinized a relatively simple phenomenon: a neuron’s firing rate is modulated when a subject performs a behavior or even mentally rehearses it, and such modulations are relatively consistent from one attempt to the other. It has become fashionable to attribute neuronal modulation to encoding various behavioral variables, such as arm movement direction. More recently, with the development of brain-computer interfaces, much work has been put into decoding information from neuronal firing rates, which strengthened the belief that neurons do encode various parameters. Yet, many researchers looked for alternative explanations of neuronal modulations rather than merely encoding. Such inquiries advanced with the development of multichannel recordings that yielded neuronal-ensemble data. Thus, in 2012, Churchland et al. published the paper entitled “Neural population dynamics during reaching” where they claimed that cortical neuronal ensembles act as dynamical system like a pendulum or a spring. In their view, neurons in such a dynamical system do not encode parameters – movement direction, muscle force etc. - but rather keep an action going. Importantly, such a dynamical system produces rhythmic, oscillatory patterns, which Churchland et al. called ‘dynamical rotations’ and plotted as circular trajectories using an analysis that they called jPCA. Since the proposed jPCA approach has become wildly popular, with the original paper getting hundreds of citations, and many follow-up publications emerging, further tackling of this method is important, and hopefully additional analyses could improve our understanding of how the brain works. Here we scrutinized the assumptions and restrictions of jPCA. By getting under the hood of jPCA we demonstrated the simplest case when it reveals rotations regardless of the data nature. It turns out that the necessary condition for rotations is hidden in the covariance matrix structure. Our work questions the unequivocal interpretation of data “rotations” and the conclusions made from it.