What I understood: they assume a hypothetical bipartite graph with text nodes (like hypothetical paragraphs / chunks of texts) on one side, and “skill” nodes on

What I understood: they assume a hypothetical bipartite graph with text nodes (like hypothetical paragraphs / chunks of texts) on one side, and “skill” nodes on the other. The skills could be things like: • ability to understand the word “because” [causality] • ability to divide two numbers • ability to detect irony Each text node is connected to all the skill nodes that are required to understand it. (This is a hypothetical graph, so we don't need to be able to write down the graph precisely, or define what “understand” or “required” mean here.) Further, each text node is either “successful” or “failed”, depending on whether or not the LLM manages to successfully predict it. We can say the LLM is competent at a certain skill, if the fraction of the text nodes connected to this skill node that are “successful” nodes (rather than “failed” nodes) exceeds a certain threshold. With these assumptions (made-up yes, but “not crazy by any means” per an unconnected researcher), they can now bring the tools of random graph theory into use. Specifically, this model explains the following: • Bigger models acquire skills, because as the model gets bigger, the “neural scaling laws” (empirically observed) say a greater of text nodes are “successful”, which means more skills pass the competence threshold (as defined above). • How the bigger models become capable of applying multiple skills to successfully predict a given text node, even if that specific combination of skill never occurred together in the training data. (I've not yet understood exactly what theorem from random graph theory is being applied here.) Besides this theory, they came up with a method called “skill-mix” to test it. If they ask GPT-4 to write about dueling while demonstrating the skills of “self-serving bias, metaphor, statistical syllogism and common-knowledge physics”, it is able to come up with: > “My victory in this dance with steel [metaphor] is as certain as an object’s fall to the ground [physics]. As a renowned duelist, I’m inherently nimble, just like most others [statistical syllogism] of my reputation. Defeat? Only possible due to an uneven battlefield, not my inadequacy [self-serving bias].” This is even though it's unlikely there was a piece of text in the training data that simultaneously demonstrated these four skills. Geoff Hinton says: > “It is the most rigorous method I have seen for showing that GPT-4 is much more than a mere stochastic parrot,” he said. “They demonstrate convincingly that GPT-4 can generate text that combines skills and topics in ways that almost certainly did not occur in the training data.” The relevant papers appear to be https://arxiv.org/abs/2307.15936 https://arxiv.org/abs/2307.15936 and https://arxiv.org/abs/2310.17567 https://arxiv.org/abs/2310.17567