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Donald Hebb states it as follows:

"Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability.… When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased." Or we can conclude in short: "Neurons that fire together, wire together".

As I understand it, this means that synapses that already exist become stronger between neurons.

  1. Could new synapses form between neighboring neurons that "fire together", but are not necessarily directly connected through an axon?
  2. And if so, what is the mechanism to direct the new synapse formation towards that other neighboring neuron that "fires together"?
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Strictly stated, Hebb's rule applies only to existing synapses, and not to the formation of new synapses. (This answer applies to biological neurons, not to ANNs).

Synapse formation is a topic of active research. During development (and in fact continuously even during adulthood), many synapses are created and destroyed. It is not unreasonable to suspect that a similar form of rule is used to decide which synapses are removed and which should remain.

Synaptic connections between neurons show a good deal of specificity -- for example, in the projection from the retina to the optic tectum, synaptic connections are made only with target neurons at an appropriate retinotopic location. This happens because growing axons follow molecular gradients.

Within a cortical column, some possible connection pathways seem to be actively sought -- for example, axo-axonal cells connect specifically to the axon initial segments of target neurons. Neurons certainly have membrane molecules that could be used to identify target cell classes.

So there are probably a number of rules used to determine when a new synapse is made. However, I am not aware of a mechanism for a pre-synaptic neuron to detect how a putative post-synaptic parter is firing, without a synapse already being present. So it seems likely that some form of random process is involved to form new synapses with reasonable post-synaptic partners, after which some activity-dependent rule (like Hebb's) could be applied.

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Keegan's answer is good I gave it an up vote. I want to offer a valid alternative.

Psychology may induce redundant pathways which trigger approximate simultaneous firing of neurons near or in completely different parts of the brain.

Emotionally intense memories can trigger emotions, basically hallucinations of the event, smells and touch based recollections. The pathways work in reverse as well actual sensory input triggering the memory. The more often you delve into your other memories the stronger your abilities to remember those events become it can be very vicious or pleasurable.

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It probably depends on what stage of development the neurons are in and what region of the brain. If there's not branching still going on, then probably not. Hebbian learning is generally considered a concept of neuron connections strengthening (more synapses forming and dendritic spines growing larger) and not the initial formation, particularly in artificial neural networks, where a non-zero weight is already assigned to the neurons, and it's just a matter of strong vs. weak connections.

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