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AbstractTo learn effectively, an adaptive controller needs to know its sensitivity derivatives — the variables that quantify how system performance depends on the commands from the controller. In the case of biological sensorimotor control, no one has explained how those derivatives themselves might be learned, and some authors suggest they aren’t learned at all but are known innately. Here I show that this knowledge can’t be solely innate, given the adaptive flexibility of neural systems. And I show how it could be learned, using forms of information transport that are available in the brain, by a mechanism I call implicit supervision. I show that implicit supervision explains a wide range of otherwise-puzzling facts about motor learning. It explains how we can cope with conditions that reverse the signs of sensitivity derivatives, e.g. nerve or muscle transpositions, reversing goggles, or tasks like drilling teeth seen in a mirror. It also explains why it is harder to recover from reversals than from other alterations such as magnifying, minifying or displacing goggles. A further prediction of the theory of implicit supervision, in its simplest form, is that each control system — say for gaze stabilization, or saccades, or reaching — has one single, all-purpose estimate of its sensitivity derivatives for all parts of the motion. When that estimate is revised, it should affect all stages of the task. For instance, when you learn to move to mirror-reversed targets then your adapted estimate of e/u should reverse not only your initial aiming but also your online course adjustments: when the target jumps in mid-movement, your path adjustment should be appropriately reversed. Here I put subjects through many trials with jumping targets, and show that, given enough practice, they do learn to reverse their course adjustments, and therefore both initial aiming and later adjustments are governed by revisable estimates of sensitivity derivatives. And I argue that all the available data, from my own experiments and earlier ones, are compatible with a single, adaptable, all-purpose estimate of these derivatives, as in the simplest form of implicit supervision.