Editing Hopfield network (section)

==Human memory==
The Hopfield network is a model for human associative learning and recall.<ref>{{cite book |last1=Amit |first1=D.J. |url=https://books.google.com/books?id=fvLYch1yQncC |title=Modeling Brain Function: The World of Attractor Neural Networks |date=1992 |publisher=Cambridge University Press |isbn=978-0-521-42124-9}}</ref><ref>{{cite book |last=Rolls |first=Edmund T. |url=https://books.google.com/books?id=on_ADAAAQBAJ |title=Cerebral Cortex: Principles of Operation |publisher=Oxford University Press |year=2016 |isbn=978-0-19-878485-2}}</ref> It accounts for [[Association (psychology)|associative]] [[memory]] through the incorporation of memory vectors. Memory vectors can be slightly used, and this would spark the retrieval of the most similar vector in the network. However, we will find out that due to this process, intrusions can occur. In associative memory for the Hopfield network, there are two types of operations: auto-association and hetero-association. The first being when a vector is associated with itself, and the latter being when two different vectors are associated in storage. Furthermore, both types of operations are possible to store within a single memory matrix, but only if that given representation matrix is not one or the other of the operations, but rather the combination (auto-associative and hetero-associative) of the two.

Hopfield's network model utilizes the same learning rule as [[Hebbian theory|Hebb's (1949) learning rule]], which characterised learning as being a result of the strengthening of the weights in cases of neuronal activity.

Rizzuto and Kahana (2001) were able to show that the neural network model can account for repetition on recall accuracy by incorporating a probabilistic-learning algorithm. During the retrieval process, no learning occurs. As a result, the weights of the network remain fixed, showing that the model is able to switch from a learning stage to a recall stage. By adding contextual drift they were able to show the rapid forgetting that occurs in a Hopfield model during a cued-recall task. The entire network contributes to the change in the activation of any single node.

McCulloch and Pitts' (1943) dynamical rule, which describes the behavior of neurons, does so in a way that shows how the activations of multiple neurons map onto the activation of a new neuron's firing rate, and how the weights of the neurons strengthen the synaptic connections between the new activated neuron (and those that activated it). Hopfield would use McCulloch–Pitts's dynamical rule in order to show how retrieval is possible in the Hopfield network. However, Hopfield would do so in a repetitious fashion. Hopfield would use a nonlinear activation function, instead of using a linear function. This would therefore create the Hopfield dynamical rule and with this, Hopfield was able to show that with the nonlinear activation function, the dynamical rule will always modify the values of the state vector in the direction of one of the stored patterns.