  Hopfield neural networks are a possible basis for modelling associative
memory in living organisms. After summarising previous studies in the field, we
take a new look at learning rules, exhibiting them as descent-type algorithms
for various cost functions. We also propose several new cost functions suitable
for learning. We discuss the role of biases (the external inputs) in the
learning process in Hopfield networks. Furthermore, we apply Newtons method for
learning memories, and experimentally compare the performances of various
learning rules. Finally, to add to the debate whether allowing connections of a
neuron to itself enhances memory capacity, we numerically investigate the
effects of self coupling.
  Keywords: Hopfield Networks, associative memory, content addressable memory,
learning rules, gradient descent, attractor networks
