  Recent physiological measurements have provided clear evidence about
scale-free avalanche brain activity and EEG spectra, feeding the classical
enigma of how such a chaotic system can ever learn or respond in a controlled
and reproducible way. Models for learning, like neural networks or perceptrons,
have traditionally avoided strong fluctuations. Conversely, we propose that
brain activity having features typical of systems at a critical point,
represents a crucial ingredient for learning. We present here a study which
provides novel insights toward the understanding of the problem. Our model is
able to reproduce quantitatively the experimentally observed critical state of
the brain and, at the same time, learns and remembers logical rules including
the exclusive OR (XOR), which has posed difficulties to several previous
attempts. We implement the model on a network with topological properties close
to the functionality network in real brains. Learning occurs via plastic
adaptation of synaptic strengths and exhibits universal features. We find that
the learning performance and the average time required to learn are controlled
by the strength of plastic adaptation, in a way independent of the specific
task assigned to the system. Even complex rules can be learned provided that
the plastic adaptation is sufficiently slow.
