I'm saying there is no "big leap" necessary. As the paper that introduced the transformer said, attention is all you need.
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In much the same way as human thinking is the second best (and soon third best) solution to any problem. The point is that an LLM can come up with the best solution and use it.
Obviously not — they're not going to make claims beyond the results they achieved in the paper. It was, however, obvious to everyone who read the paper that all of what we consider thinking could be derived by clever application of a sequence model, and all those papers that came after were results achieved by teams doing the obvious thing.