Impact of redundancy on stable decoding

[get notes as PDF]

Neural activity is redundant: many states in motor cortex can generate similar movements. When we record from motor cortex, we capture only a small fraction of the total neurons. Redundancy makes it possible to observe the overall state of motor cortex from limited observations, but might also impair the generalization performance of a linear decoder.

Consider two neurons, $A$ and $B$, that combine linearly to produce movement $C{=}\alpha_1 A{+} \alpha_2 B$. (Perhaps both neurons drive the same targets in spinal cord.) An animal could use any linear combination of activations of units $A$ and $B$ to perform behavior $C$, so long as the sum $\alpha_1{+}\alpha_2$ is constant. What if there is an unobserved variable $\gamma$ that sets whether neuron $A$ or $B$ is used more (Fig. 1)?

Figure 1: (simulated hypothetical scenario) Neural signals $A$ and $B$ combine linearly according to weight $\gamma$ to form behavioral output $C=\gamma A + (1-\gamma) B$. Parameter $\gamma$ modulates sinusoidally between $0.25$ and $0.75$.

Impact of fast and slow neuronal variability in output-null dimensions on motor decoding

[get these notes as PDF]

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.