The Boltzmann machine
Ackley, Hinton and Sejnowski described a network of stochastic units with a hidden layer, trainable by a rule that compares two modes of operation.
Why it matters
Hidden layers first acquired a training rule with a clear statistical justification, a year before back-propagation.
The network has an energy like Hopfield's, but its states switch probabilistically under a temperature. The learning rule compares statistics with the input clamped against statistics of free running and shifts the weights by the difference. Training is extremely slow because it needs equilibrium. The restricted Boltzmann machine from the same line later gave Hinton his 2006 method for pre-training deep networks.