Editing Hopfield network (section)

===Storkey learning rule===
This rule was introduced by [[Amos Storkey]] in 1997 and is both local and incremental. Storkey also showed that a Hopfield network trained using this rule has a greater capacity than a corresponding network trained using the Hebbian rule.<ref name="storkey1997">{{cite book |last=Storkey |first=Amos |chapter=Increasing the capacity of a Hopfield network without sacrificing functionality |title=Artificial Neural Networks – ICANN'97 |year=1997 |citeseerx=10.1.1.33.103 |pages=451–6 |doi=10.1007/BFb0020196 |publisher=Springer |series= Lecture Notes in Computer Science |volume=1327 |isbn=978-3-540-69620-9}}</ref> The weight matrix of an attractor neural network{{clarify|reason=What is an attractor NN?|date=July 2019}} is said to follow the Storkey learning rule if it obeys:

<math> w_{ij}^{\nu} = w_{ij}^{\nu-1}
		    +\frac{1}{n}\epsilon_{i}^{\nu} \epsilon_{j}^{\nu} 
		    -\frac{1}{n}\epsilon_{i}^{\nu} h_{ji}^{\nu}
		    -\frac{1}{n}\epsilon_{j}^{\nu} h_{ij}^{\nu}
		    </math>

where <math> h_{ij}^{\nu} = \sum_{k=1~:~i\neq k\neq j}^{n} w_{ik}^{\nu-1}\epsilon_{k}^{\nu} </math> is a form of ''local field''<ref name="storkey1991basins">{{cite journal |last1=Storkey |first1=A.J. |first2=R. |last2=Valabregue |title=The basins of attraction of a new Hopfield learning rule |journal=Neural Networks |volume=12 |issue=6 |pages=869–876 |year=1999 |doi=10.1016/S0893-6080(99)00038-6 |pmid=12662662 |citeseerx=10.1.1.19.4681}}</ref> at neuron i.
		    
This learning rule is local, since the synapses take into account only neurons at their sides. The rule makes use of more information from the patterns and weights than the generalized Hebbian rule, due to the effect of the local field.