  Information measures are often used to assess the efficacy of neural
networks, and learning rules can be derived through optimization procedures on
such measures. In biological neural networks, computation is restricted by the
amount of available resources. Considering energy restrictions, it is thus
reasonable to balance information processing efficacy with energy consumption.
Here, we studied networks of non-linear Hawkes neurons and assessed the
information flow through these networks using mutual information. We then
applied gradient descent for a combination of mutual information and energetic
costs to obtain a learning rule. Through this procedure, we obtained a rule
containing a sliding threshold, similar to the Bienenstock-Cooper-Munro rule.
The rule contains terms local in time and in space plus one global variable
common to the whole network. The rule thus belongs to so-called three-factor
rules and the global variable could be related to a number of biological
processes. In neural networks using this learning rule, frequent inputs get
mapped onto low energy orbits of the network while rare inputs aren't learned.
