A Hebbian learning rule gives rise to mirror neurons and links them to control theoretic inverse models.

Mirror neurons are neurons whose responses to the observation of a motor act resemble responses measured during production of that act. Computationally, mirror neurons have been viewed as evidence for the existence of internal inverse models. Such models, rooted within control theory, map-desired sensory targets onto the motor commands required to generate those targets. To jointly explore both the formation of mirrored responses and their functional contribution to inverse models, we develop a correlation-based theory of interactions between a sensory and a motor area. We show that a simple eligibility-weighted Hebbian learning rule, operating within a sensorimotor loop during motor explorations and stabilized by heterosynaptic competition, naturally gives rise to mirror neurons as well as control theoretic inverse models encoded in the synaptic weights from sensory to motor neurons. Crucially, we find that the correlational structure or stereotypy of the neural code underlying motor explorations determines the nature of the learned inverse model: random motor codes lead to causal inverses that map sensory activity patterns to their motor causes; such inverses are maximally useful, by allowing the imitation of arbitrary sensory target sequences. By contrast, stereotyped motor codes lead to less useful predictive inverses that map sensory activity to future motor actions. Our theory generalizes previous work on inverse models by showing that such models can be learned in a simple Hebbian framework without the need for error signals or backpropagation, and it makes new conceptual connections between the causal nature of inverse models, the statistical structure of motor variability, and the time-lag between sensory and motor responses of mirror neurons. Applied to bird song learning, our theory can account for puzzling aspects of the song system, including necessity of sensorimotor gating and selectivity of auditory responses to bird's own song (BOS) stimuli.