The 'Hebbian synapse', an old neuro-psychological concept which describes t
he process of associative learning at the synaptic level, is being increasi
ngly confirmed by neuro-biological explanations. The purpose of the present
paper is to show that sensorimotor learning, which is essentially non-asso
ciative, can also be explained by Hebbian learning. This requires a redefin
ition of the Hebbian synapse ensuring convergence of the synaptic weight. R
e-defined Hebbian learning then appears as a linear adaptive filter known i
n the field of adaptive signal processing, which in turn is equivalent to t
he delta rule used to train artificial neural networks. For motor learning,
the modified Hebbian synapse must be embedded into a special learning algo
rithm called 'auto-imitation', This is a non goal-oriented inductive learni
ng algorithm, enabling a controller to adopt a general rule from being show
n only a Few examples of that rule. When applied to motor learning, the neu
ral controller can acquire the capability to online invert the behavior of
the plant to be controlled. The complete learning process then can be descr
ibed as a relaxation process between the controller and the controlled syst
em, which is governed by long-term potentiation (LTP), the neuro-physiologi
cal process underlying Hebbian synaptic shaping. (C) 1999 Elsevier Science
B.V. All rights reserved.