  Memristors, resistors with memory whose outputs depend on the history of
their inputs, have been used with success in neuromorphic architectures,
particularly as synapses and non-volatile memories. However, to the best of our
knowledge, no model for a network in which both the synapses and the neurons
are implemented using memristors has been proposed so far. In the present work
we introduce models for single and multilayer perceptrons based exclusively on
memristors. We adapt the delta rule to the memristor-based single-layer
perceptron and the backpropagation algorithm to the memristor-based multilayer
perceptron. Our results show that both perform as expected for perceptrons,
including satisfying Minsky-Papert's theorem. As a consequence of the Universal
Approximation Theorem, they also show that memristors are universal function
approximators. By using memristors for both the neurons and the synapses, our
models pave the way for novel memristor-based neural network architectures and
algorithms. A neural network based on memristors could show advantages in terms
of energy conservation and open up possibilities for other learning systems to
be adapted to a memristor-based paradigm, both in the classical and quantum
learning realms.
