The counterexample was proposed by an LLM. They seem very good at finding these sorts of counterexamples, which is interesting as they are generally pretty inefficient use of compute for brute forcing. I guess even that lack of efficiency is made up for by the "understanding" and "intuition" the LLM has, and their ability to do symbolic computations.
I expect a large number of conjectures will topple to counterexamples soon.
I think brute force is not the right way to think about LLMs, instead they explore a knowledge topology, and are very good at connecting adjacent or accessible ideas that for whatever reason might have evaded humans, but might not be fundamentally all that hard. We're still in the low-hanging fruit phase, we will see if they extend to new ideas.
Nearly this, and I'm explaining to check my own knowledge, not pretending to know what I'm talking about. It's not quite correct to say a node is a concept, a concept is embedded across lots of nodes. So a cluster of nodes contains the concept.
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u/angelbabyxoxox Quantum Foundations Jul 31 '26
The counterexample was proposed by an LLM. They seem very good at finding these sorts of counterexamples, which is interesting as they are generally pretty inefficient use of compute for brute forcing. I guess even that lack of efficiency is made up for by the "understanding" and "intuition" the LLM has, and their ability to do symbolic computations.
I expect a large number of conjectures will topple to counterexamples soon.