So every neural network is actually entertained in an astrocytic syncitium. Every synapse is being "listened to" and modulated by it's astrocytic end foot (which forms the third arm of what we now call the tripartite synapse).
If neurons are about breaking down signals, the astrocytes are the slow, steady integrators that (potentially) can serve as the global workspace that scientists have been theorizing but not yet found.
So there actually is a problem with modern neural networks, in so far as comparisons with human brains go: they're missing the design spec for literally half of it.
Which is fine. Connectionist models come from a time when the height of neuroscience said neurons were the bees knees and glia were just support staff. Today, astrocytes, and other glia, are forcefully back in the conversation. And they don't seem to do anything like neural networks.