The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World

by Pedro Domingos

For one, spin interactions are symmetric, and connections between neurons in the brain are not. Another big issue that Hopfield’s model ignored is that real neurons are statistical: they don’t deterministically turn on and off as a function of their inputs; rather, as the weighted sum of inputs increases, the neuron becomes more likely to fire, but it’s not certain that it will. In 1985, David Ackley, Geoff Hinton, and Terry Sejnowski replaced the deterministic neurons in Hopfield networks with probabilistic ones. A neural network now had a probability distribution over its states, with higher-energy states being exponentially less likely than lower-energy ones. In fact, the probability of finding the network in a particular state was given by the well-known Boltzmann distribution from thermodynamics, so they called their network a Boltzmann machine.