Hebbian theory &Hebbian Learning Rule

Hebbian theory :
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. (D.O. Hebb, The organization of behavior: a neuropsychological theory, p.62,Wiley, New York (1949).)


Hebbian Learning Rule :
The Hebbian Learning Rule is a learning rule that specifies how much the weight of the connection between two units should be increased or decreased in proportion to the product of their activation. The rule builds on Hebbs's 1949 learning rule which states that the connections between two neurons might be strengthened if the neurons fire simultaneously. The Hebbian Rule works well as long as all the input patterns are orthogonal or uncorrelated. The requirement of orthogonality places serious limitations on the Hebbian Learning Rule. A more powerful learning rule is the delta rule, which utilizes the discrepancy between the desired and actual output of each output unit to change the weights feeding into it.
（Bechtel, W., & Abrahamsen, A. (1993). Connectionism and the mind. Oxford, UK: Blackwell.
Hebb, D.O. (1949) The organization of behavior. New York: Wiley.
Rumelhart, D.E., & McClelland, J. L. and the PDP Research Group (1986). Parallel Distributed Processing: Explorations in the microstructure of cognition, vol. 1: Foundations, Cambridge, MA: MIT Press/Bradford Books.）