CoachHebb (1949) proposed that when a presynaptic neuron repeatedly takes part in firing a postsynaptic one, the connection between them is strengthened — “cells that fire together wire together”. Long-term potentiation (LTP) is its experimental form: a brief burst of high-frequency stimulation of a pathway leaves the synapses it activated stronger for hours in a slice and for weeks in an animal. LTP is input-specific (only the stimulated synapses change), associative (a weak input paired with a strong one to the same cell is potentiated) and needs cooperativity among inputs to depolarise the cell. Long-term depression (LTD) is its opposite, produced by prolonged low-frequency activity. In spike-timing-dependent plasticity the sign is set by order: a presynaptic spike a few milliseconds before the postsynaptic one strengthens the synapse, one just after weakens it, within a window of about on either side — so that a synapse learns to predict, not merely to correlate.
Examples
Example 19.5 (Two inputs)
A neuron receives two inputs that are usually active together, so . The eigenvectors are with eigenvalue and with eigenvalue . Starting from , Hebb’s rule after many small steps turns toward : the neuron learns to respond to the two inputs together, and to ignore the rare occasions on which only one fires — it has extracted the correlation. With Oja’s rule the weights settle at . This is the sense in which Hebbian synapses learn what goes together, and it is why the associative property of LTP, pairing a weak input with a strong one, follows from the rule.