Binary Hopfield net using Hebbian learning We want to study Hopfield net from the simple case. Hopfield net is a fully connected feedback network. A feedback network is a network that is not a feedforward network, and in a feedforward network, all the connections are directed. All the connections in our example will be bi-directed. This symmetric property of the weight is important property of the Hopfield net. Hopfield net can act as associative memories, and they can be used to solve optimization problems.

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Why Ising model : 3 reasons for relevance Studying Ising model can be useful to understand phase transition of various systems. Hopfield network or Boltzmann machine to the neural network is just a generalized form of Ising model. Ising model is also useful as a statistical model in its own right. Ising model $\boldsymbol{x}$ is the state of an Ising model with $N$ spins be a vector in which each component $\boldsymbol x_n$ takes values $-1$ or $+1$.

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