# Hebbian learning rule

The Hebbian learning rule is a rule established by the psychologist Donald Olding Hebb for the creation of learning in neural networks or in general in a group of neurons that have common synapses .

## history

Hebb formulated in 1949 in his book The Organization of Behavior : “If an axon of cell A […] excites cell B and repeatedly and permanently contributes to the generation of action potentials in cell B, this results in growth processes or metabolic changes in one or both Cells that have the effect that the efficiency of cell A with regard to the generation of an action potential in B increases. "

This means: the more often a neuron A is active at the same time as neuron B, the more preferentially the two neurons will react to each other (“what fires together, wires together”). Hebb has demonstrated this on the basis of changes in synaptic transmission between neurons.

The experiments of Terje Lømo and others in the 1960s and 1970s and the direct evidence of the change in signal transmission as part of the mechanism for learning processes and memory in 2014 are considered to be the final confirmation of Hebb's theses .

Hebb is thus considered to be the discoverer of the model of synaptic plasticity , which represents the neurophysiological basis of learning and memory.

## formula

In artificial neural networks , this change in synaptic transmission is mapped as a weight change in the neural graph. The Hebrew learning rule is the oldest and simplest neural learning rule.

${\ displaystyle \ Delta w_ {ij} = \ eta \ cdot a_ {i} \ cdot a_ {j}}$

With

• ${\ displaystyle \ Delta w_ {ij}}$: Change in the weight of neuron i to neuron j (i.e. the change in the strength of the connection between these two neurons)
• ${\ displaystyle \ eta}$: Learning rate (a suitable constant factor to be chosen)
• ${\ displaystyle a_ {i}}$: Activation of neuron i
• ${\ displaystyle a_ {j}}$: Activation of neuron j connected to neuron i.

## Individual evidence

1. ^ TV Bliss, T. Lomo: Long-lasting potentiation of synaptic transmission in the dentate area of ​​the anesthetized rabbit following stimulation of the perforant path. In: J Physiol. 232 (2), 1973, pp. 331-356, Free Full Text Online. PMID 4727084
2. G. Yang, CS Lai, J. Cichon, L. Ma, W. Li, WB Gan: Sleep promotes branch-specific formation of dendritic spines after learning. In: Science. 344 (6188), 2014, pp. 1173-1178. PMID 24904169
3. Manfred Spitzer : Spirit in the net, models for learning, thinking and acting . Spektrum Akademischer Verlag, Heidelberg 1996, ISBN 3-8274-0109-7 , p. 107.

## literature

• Donald Hebb : The organization of behavior. A neuropsychological theory . Erlbaum Books, Mahwah, NJ 2002, ISBN 0-8058-4300-0 (reprint of New York 1949 edition)