The interest in neuronal networks originates for a good part in the option not to construct, but to train them. The mechanisms governing synaptic modifications during such training are assumed to depend on signals locally available at the synapses. In contrast, the performance of a network is suitably measured on a global scale. Here we propose a learning rule that addresses this conflict. It is inspired by recent physiological experiments and exploits the interaction of inhibitory input and backpropagating action potentials in pyramidal neurons. This mechanism makes information on the global scale available as a local signal. As a result, several desirable features can be combined: the learning rule allows fast synaptic modifications approaching one-shot learning. Nevertheless, it leads to stable representations during ongoing learning. Furthermore, the response properties of the neurons are not globally correlated, but cover the whole stimulus space.