Output-null spaces in motor control
The idea of a null-space extends the notion of selectivity and invariance to motor cortex (Kaufman et al. 2010). Rather than asking what stimuli change the firing rate of a neuron (and what stimulus changes it is in variant to), we ask what neural activity drives movement (and what activity does not). The subspace in which neural activity in motor cortex can vary without changing behavior is called the "output-null" space.
Variables in the output-null space explains neural variability not related to an observed behavior. This residual variability may contain components related to unmeasured behavior, neural processing, and noise sources. If one has observations from behavior $X$ and output-null space $Z$, then neural covariates $Y$ are determined. Neural variability factors in to variability induced by behavior, and that induced by output-null space.
