Hopfield Network - Human Memory

Human Memory

The Hopfield model accounts for 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. It is important to note that Hopfield’s network model utilizes the same learning rule as Hebb’s (1949) learning rule, which basically tried to show that learning occurs as a result of the strengthening of the weights by when activity is occurring.

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 remains fixed, showing that the model is able to switch from a learning stage to a recall stage. By adding contextual drift we are 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.

The Network capacity of the Hopfield network model is determined by neuron amounts and connections within a given network. Therefore, the number of memories that are able to be stored are dependent on neurons and connections. Furthermore, it was shown that the recall accuracy between vectors and nodes was .138 (approximately 138 vectors can be recalled from storage for every 1000 nodes) (Hertz et al., 1991). Therefore, it is evident that many mistakes will occur if you try to store a large number of vectors. When the Hopfield model does not recall the right pattern, it is possible that an intrusion has taken place, since semantically related items tend to confuse the individual, and recollection of the wrong pattern occurs. Therefore, the Hopfield network model is shown to confuse one stored item with that of another upon retrieval. But this can be improved before applying the dynamical rule (which is explained in the next paragraph) and adding some noise to the activations.

McCullough 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 McCullough-Pitts's dynamical rule in order to show how retrieval is possible in the Hopfield network. However, it is important to note that 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.