Looking into the Hopfiled Network
The Hopfield network, suggested by John J. Hopfield in 1982, is a physical model of neural network. It is used in optimization and associated memory.
This network represents the bi-directional connection among neural circuit network.
It receives binary inputs(0.1) and gives out positive(+) and negative(-) energy state.
This model consists of algorithms below.
Here the pattern(rule) of learning A1 and A2 are given. This pattern has already been calculated from the former learning.
The first step of the Hopfield Network is to polarize(amplify) the existing pattern. This is to make sure it matches the desired state. 
The next step is to find the weight matrix. The equation below is the function needed to calculate the weight matrix.
n is the number of existing patterns. Here, n is 2, (x1 and x2). I is the identity matrix 
If we calculate W,
Now, comes in the new input pattern. More precisely, a new pattern is "suggested”. 
We intend to find out how much this new input matches the existing learning patten.
For the calculation, we use the function below.
First, we find the threshold. This threshold is adapted when we can not find the matching pattern.
Apply weight to the input matrix, then, add the threshold.
Finally, it is time for the neuron to kick in. The activation function is in charge of this neuron’s work.
Now, we have the modified pattern through Hopfield network. We can see that this pattern matches one of the existing learning rule.
Then, this matching pattern is associated without further repetition. In other words, it judges that this pattern matches the desired learning rule. 
If it does not match with any existing learning rule, threshold is further adapted to find out the similarity with the existing rules
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