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With filters you have feed-forward components and feed-back components. Feedback takes the result of your filter, modifies it somehow (typically by multiplying by a scalar coefficient) and then delays it by some amount before taking that value and feeding it back into your filter. Feed forward is the same concept except it's the input going to your filter (or some combination of inputs; also combinations of inputs at different relative points in time).
So feedforward error prediction is simply a scheme where I have one set of coefficients (e.g. a polynomial or whatever based on past values of the input) that are used to predict some "state" and then I have some other thing that gives me the actual "state" (in the brain, this could be sensory signals that will arrive LATER than the predicted signal). The error is the discrepancy between what is sensed by the sensory signals and what was predicted by the feedforward signal.
A lot of the feedback correction happens in cerebellar circuits; however, the forward-component (prediction) is thought to occur in cortical circuitry- it makes sense because if motor cortex is controlling the behavior, then motor cortex should have some "concept" of where the hand is in space at any given instant (even if it's not completely accurate)
What is a feedforward error predicting scheme? Mentioned in the abstract.
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