### Why Hopfield networks?

Hopfield Networks are certainly nothing new in the field of neural
networks. The amount of research which involves Hopfield-like networks
has reduced substantially over the last decade. It can be argued that
Hopfield networks do not have any natural applications. Some have
argued that they make associative memories, or are an optimisation
tool. However they are relatively inefficient, unreliable and
unprincipled at both these tasks.

Others argue that Hopfield networks form solvable models and analogies
of brain activity. However the cost of the simplicity of the Hopfield
model is a very poor representation of anything like real neural
behaviour. Yes, analogies provided by Hopfield models can be helpful,
but they rarely progress to anything more concrete.

So why might anyone be interested in Hopfield networks? Well the
simple answer is that they provide some hard but solvable puzzles. The
similarity of stochastic Hopfield systems to spin-glasses in physics
has meant that many of the techniques of that field have be used to
characterise something of the structure of the Hopfield network. And
this structure is very interesting. Hence most of the research in Hopfield
networks has been motivated by an interest in the dynamical or
stochastic systems which Hopfield networks represent, and an interest
in the techniques that are used to solve them.

Does this mean that research into Hopfield networks is esoteric and of
no practical use? Not entirely no. As is often the case with the study
of certain systems, the structures and techniques used with Hopfield
networks can crop up in a host of different places, from the use of
chi-squared process models to learning methods in adaptations of
hidden markov models. These methods work within an appropriate Bayesian
framework, and do not follow the original ad-hoc form of the
Hopfield associative memory. This is work in progress.

Here is an outline of old research in Hopfield networks.

A new class of learning rules for Hopfield networks, which have high
capacity and functionality. They also have palimpsest properties. Palimpsest rules have interesting learning properties. The forget old
memories in order to learn new ones. These learning rules can be
analysed in terms of iterated function systems.

Ways of looking at the capacity of the new learning rules.