A neural network or artificial neural network, also simply known as a neural net, was a network or circuit of neurons, either biological or artificial, respectively. An artificial neural network dealt with artificial intelligence, such as the positronic brain inside Soong-type androids.
In 2366, nanites entered android Lieutenant Commander Data's neural network and used him as a conduit for negotiation aboard the USS Enterprise-D. The nanites requested relocation as the vessel had become too confining. Doctor Paul Stubbs used his influence to have the planet Kavis Alpha IV designated the new home of the nanites' civilization. Data's neural network was vacated and he was returned unharmed. (TNG: "Evolution")