# Intellectics Group: Technical Report 96-08

## Multi-Flip Networks: Extending Symmetric Networks to Real Parallelism

### Antje Strohmaier

In general, neural networks are regarded as models for massively
parallel computation. But very often, this parallelism is rather
limited, especially when considering symmetric networks. For
instance, Hopfield networks do not *really* compute in
parallel as their updating algorithm always requires sequential
execution. Nevertheless, Hopfield networks can be used as
auto-associative memories, were shown to have an expressive power
equivalent to propositional logic, and can be used to solve several
combinatorial problems. Extensions like the Boltzmann Machine with
continuous activation functions can additionally be used to solve
optimization problems. But, all of these approaches suffer from
one disadvantage, namely the impossibility to perform simultaneous
computations of more than one unit, i.e. real parallelism. We
describe a recurrent network corresponding to a symmetric network
and introduce a method of parallel updating multiple units. We
show how this may be extended to Boltzmann machines with
continuous activation functions, and point out possible
applications of this architecture.