Electrophysiological research on the properties of the apical dendrites of cortical deep layer pyramidal cells suggests that it acts, in addition to the soma, as a second site of synaptic integration. Each site integrates input from a subset of synapses and is able to generate regenerative potentials. The sites exchange information in stereotyped ways: Signals from the soma are transmitted to the apical dendrite via actively back-propagating dendritic action potentials. Slow regenerative calcium spikes transmit information from the apical dendrite to the soma. These calcium spikes lead to a strong and prolonged depolarization of the cell generating a burst of action potentials. This paper analyzes how the system learns if these calcium spikes trigger Hebbian learning at active synapses. A cell is now described by two main variables the mean activity and the mean potential at the apical dendrite with the first variable defining the input to cells downstream and the latter what the cell learns. A system results where neurons learn to respond to those features that are correlated with activity on the higher layer, this property is similar to maximizing the mutual information between input and higher areas. Furthermore, it learns invariances exploiting a spatial smoothness criterion.