# MoN11: Elevent Mathematics of Networks meeting, 20th July University of Warwick

## Gordon Govan (Herriot-Watt University) – A critical study of network models for neural networks

In this research we take a critical look at the network models used to
replicate neural networks. As case study we consider the neural network of C.
elegans. In the following we refer to this network as the target network. We
chose this network because it is relatively small (306 nodes and approximately
9000 edges), its topology is completely known and it has been extensively used
as a benchmark for several studies. We computed several topological features
of this neural network and we tested its dynamics under different stimuli when
it is regarded as a random recurrent neural network. Then, using known network
models, we generated networks having topological features as similar as
possible to our case study, we treated these networks as random recurrent
neural networks, and we tested their dynamics under different stimuli.

We found out that there is very little relation between similarities in
dynamics and similarities in topology between our case study and the generated
networks. This means that similar dynamics between a particular generated
network and the target network do not imply similar topology. Also the
opposite does not hold true: artificial networks having topological features
similar to the target network do not share similar dynamics.

The present research poses more questions than it actually answers and,
overall, our findings can be summarised saying that none of the current network
models seem to be appropriate to replicate the target network. If one wants to
have networks similar (both in topology and dynamics) to the target network,
then it is better to obtain other network simply perturbing (i.e., applying a
filter/noise) the edges of the target network. Put in different terms, this
research let us realise even more the pitfalls in which it is possible to fall
when trying to replicate complex networks.

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Contact:
Keith Briggs
()
or
Richard G. Clegg (richard@richardclegg.org)