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)?
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| 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 $0.75$. |
Let's say we record only from neuron $A$. Building a linear decoder $\hat C = \alpha A$ leads to an over-fit (and erroneous) estimate of the contribution of $A$ to behavior: $\hat\alpha = (A \cdot C)/(A \cdot A) \approx 0.996$. When predicting behavior from $A$, the reconstruction error varies depending on the unobserved slow variable $\gamma$ (figure 2). This error resembles transient noise, or perhaps an independent source of neuronal variability. But, the activation of $A$ and $B$ always drives behavior in a predictable way. Hidden sources of variability, and under-sampling of the neural population, leads to apparent instability when there is none (Fig. 2).
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| Figure 2: (simulated hypothetical scenario) (A) Reconstructed behavior using only unit $A$ leads to unstable decoding accuracy. (B) The the smoothed (Gaussian kernel σ=60 ms) absolute reconstruction error varies with this hidden parameter $\gamma$, which sets $A$'s contribution to the motor output. |
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