If you'd consider all the devices on which the virtual assistent runs as individual nodes, you could say those, together with the servers which run in the background, form a neural network. Definition according to Merriam Webster Dictionary:
"a computer architecture in which a number of processors are interconnected in a manner suggestive of the connections between neurons in a human brain and which is able to learn by a process of trial and error — called also neural net"1
Parallels with neural networks in computer science
The picture below shows a simple neural network as used in computer science. It consists of input, output and hidden nodes. One could draw the parallel to this question, arguing that the user's devices serve the roles of both input and output nodes (because there is no actual physical part). The architecture behind it (processing power on different servers, machine learning applications which turn the input into the most optimal output) could be referred to as the hidden nodes.
Source attribution for this picture can be found under 2 below.
1 "Neural Network." Merriam-Webster.com. Accessed March 20, 2018. https://www.merriam-webster.com/dictionary/neural network.
2 By en:User:Cburnett [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons