Adaptive learning by extremal dynamics and negative feedback
  We describe a mechanism for biological learning and adaptation based on two simple principles: (I) Neuronal activity propagates only through the network's strongest synaptic connections (extremal dynamics), and (II) The strengths of active synapses are reduced if mistakes are made, otherwise no changes occur (negative feedback). The balancing of those two tendencies typically shapes a synaptic landscape with configurations which are barely stable, and therefore highly flexible. This allows for swift adaptation to new situations. Recollection of past successes is achieved by punishing synapses which have once participated in activity associated with successful outputs much less than neurons that have never been successful. Despite its simplicity, the model can readily learn to solve complicated nonlinear tasks, even in the presence of noise. In particular, the learning time for the benchmark parity problem scales algebraically with the problem size N, with an exponent $k\sim 1.4$. 
Per Bak and Dante R Chialvo