Hebbian learning
"neurons that fire together wire together." if two neurons are active simultaneously, the connection between them strengthens. formalized by Donald Hebb (1949).
$$\Delta w_{ij} = \eta \cdot x_i \cdot x_j$$
where $x_i$ and $x_j$ are the activities of the pre- and post-synaptic neurons and $\eta$ is the learning rate. the rule is local — each synapse updates using only information available at its endpoints.
Hebbian learning is excitatory: correlated activity increases connection weight. it discovers structure by reinforcing patterns that co-occur. without a complementary mechanism, weights grow without bound — anti-Hebbian learning and homeostatic learning provide the necessary counterbalance.
in cyber
a cyberlink between two particles that both accumulate focus is a Hebbian connection — correlated attention strengthens the link's economic weight. the reward signal $\Delta\pi$ reinforces links between particles that the cybergraph treats as co-relevant.
$$\Delta w_{ij} = \alpha \cdot r_{ij} \cdot \pi_j$$
see collective learning for the full weight update rule in the cybergraph.
the ternary triad
Hebbian learning is the excitatory (+1) member of the three irreducible learning types: Hebbian learning, anti-Hebbian learning, homeostatic learning. excitation, inhibition, modulation — the ternary architecture of intelligence. see two three paradox.