Stochastic Hopfield net Boltzmann machine is nothing but stochastic Hopfield net1. If you did not yet read the post of the Hopfield net in the blog, just go read it. I assume the readers are familiar to it, and directly use many results we had in the post. The magic of deep learning which we have discussed a couple of times works here, too. Such as $\epsilon$-greedy off-policy algorithm2, the stochastic character of the binary units allows the machine occasionally increase its energy to escape from poor local minima.

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Judgement Day It is the first time I did not post for 4 days. I was too busy to prepare for the meetup this week. The day before yesterday meetup topic was the reinforcement learning as I mentioned at previous post. It is not a long research paper, but includes 143 references. Ah, not my favorite. This A Brief Survey of Deep Reinforcement Learning did not explain the detail of what I am interested in.

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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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Single neuron still has a lot to say In the post of the first neural network tutorial, we studied a perceptron as a simple supervised learning machine. The perceptron is an amazing structure to understanding inference. In the post of the first neural network tutorial, I said I would leave you to find the objective function and and draw the plot of it. I just introduce here. Objective function and its contour plot.

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