Minimal Hebbian Rule
Is the [see page 12, quintessential] hebbian rule based around Hebbs postulum.
\begin{align} \Delta{w_{ij}} = \alpha v_i^{\text{post}} v_j^{\text{pre}} \end{align}
Which states that the weight of a synaptic connection between a pre-synaptic neuron \( j \) and a post-synaptic neuron \( i \) should be proportional to the product of both neurons output-potential. \( \alpha \) in the above equation is some non-negative constant and is used as a learning-rate.
Note By this minimalist definition we only change the weights for a neuron when both its input neuron and itself is firing. If either the output or input potential is 0 then the change in weights will also be 0.