Lenka Zdeborová


"They allow you to understand what the phase transition is actually about. This allowed us to understand that magnetism is about atoms aligning: In one phase, the overall alignment is big, and in the other (nonmagnetic) phase, there is no alignment.

"That’s the beautiful thing that appeared in our mathematical description of the language models. There were two order parameters, each with a precise meaning. One determined if the learning that happens relies a lot on the position of the words in the sentence. The other order parameter was specifically about the meaning of each word, the semantics.

"And when we looked at the phase transition, we found that below a certain threshold of training examples, only the position mattered —not the semantics. And if we had more examples above that threshold, it was only the semantics that mattered. So, in a sense, it’s a new type of phase transition between positional and semantic learning that we could characterize in a simplified language model. 

"To me, this is a baby step toward understanding emergent properties in large language models, like suddenly being able to do arithmetic, answer questions in Greek, or things like that."


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