Hi! ILE/IEE here (unsure of which)

I've been reading the book "Thinking Fast and Slow" by Daniel Kahneman which seems to be an attempt on his part to analyze the structure of human decision making. The metaphor that he employs to examine the functioning the brain is one that splits it into a dichotomy of systems - System 1 and System 2, the former of which is concerned with "intuitions" (read: preconceived notions formed over exposition to phenomena over time) and the latter of which is concerned with more statistical or rational analysis of these intuitions. He argues that System 1 is what humans use on autopilot most of the time and that it is prone to passing down incomplete associations to System 2 for analysis, and that a part of self-awareness is conscious of your own irrationality.

What I found particularly interesting was that my conception of the way a neural network works seems to be heavily analogous to the way Kahneman's System 1 works: an associative system that attempts to immediately categorize new input appropriately based on pre-processed prior input: similar to what a lot of cognitive psychologists seem to regard as "intuition". What I see is very little System 2: from my experience, the neural network algorithms I have seen are not as exacting and precise as they are associative and pattern-matching.
Intuitively speaking, this means that it's far easier to have a neural network that is adapted towards one purpose or one method of categorization: not many I have seen attempt to fill the role of a "general AI" that can perform any computation or fill any association. The problem I'm pondering, however, is if it's currently within the realm of possibility to have a neural network specifically suited to the purpose of ideation; that is to say, a neural network that possesses the ability of creative thought, something that thus far seems to be restricted to the domain of humans.
I feel like a fraud if I don't precisely define what exactly I mean by creative thought. Once again, Kahneman argues (with reference to another author whose name seems to escape me, I apologize) that creativity consists mainly of highly developed associative thought - the refined ability to draw analogies between disparate contexts to reach new insights, drawing on an "intuition" (or in the case of a neural network, the pre-determined data). So for a rather stereotypical example, the ability to relate a table and the sun. I intuit that such an algorithm would require control over how exactly the associations are made and the expanse of the context and also requires a precise prompt to determine which idea exactly to have.
TL;DR is it possible to create an neural network that draws on what it's learned and links it to realize new ideas rather than just calculate or categorize things? Let's brainstorm and get this discussion going!