  In this paper, we introduce elements of probabilistic model that is suitable
for modeling of learning algorithms in biologically plausible artificial neural
networks framework. Model is based on two of the main concepts in quantum
physics - a density matrix and the Born rule. As an example, we will show that
proposed probabilistic interpretation is suitable for modeling of on-line
learning algorithms for PSA, which are preferably realized by a parallel
hardware based on very simple computational units. Proposed concept (model) can
be used in the context of improving algorithm convergence speed, learning
factor choice, or input signal scale robustness. We are going to see how the
Born rule and the Hebbian learning rule are connected
