Recap of probability theory: conditional probabilities, Bayes’ theorem with several examples. Statistical inference.

Supervised learning: the perceptron. AND, OR and XOR functions. The perceptron learning rule.

Gradient descent learning. Learning as inference.

Multi-layer networks: XOR function; error back-propagation. Deep learning.

Unsupervised learning: Principal Component Analysis, Oja’s rule.

Recap of statistical mechanics: ensembles, statistical entropy, Ising model with nearest neighbor interactions.

Auto-associative memory and attractor neural networks. Hebbian learning rule, synaptic plasticity. Memory as an Ising model: the Hopfield network. Statistical mechanics of the Hopfield network.

Computation of the capacity of the Hopfield network using mean field theory. Absence of spurious retrieval states; phase diagram in the temperature-storage plane. The brain as an anticipating machine: Boltzmann machines, Helmholtz machines learn probability distributions. Wake and sleep learning rule.

Backpropagation through time. Reinforcement learning.

The temporal credit assignment problem and its solution using temporal difference learning. The actor/critic model.