They are trained to predict next tokens in a stream.
That is the learning algorithm.
The algorithm they learn, in response, is quite different. Since that learned algorithm is based on the training data.
In this case the models learn to sensibly continue text or conversations. And they are doing it so well it’s clear they have learned to “reason” at an astonishing level.
Sometimes, not as good as a human.
But in a tremendous number of ways they are better.
Try writing an essay about the many-worlds interpretation of the quantum field equation, from the perspective of Schrödinger, with references to his personal experiences, using analogies with medical situations, formatted as a brief for the Supreme Court, in Dr. Seuss prose, in a random human language of choice.
In real time.
While these models have some trouble with long chains of reasoning, and reasoning about things they don’t have experiences (different modalities, although sometimes they are surprisingly good), it is clear that they can also reason combining complex information drawn from there whole knowledge base much faster and sensibly than any human has ever come close to.
Where they exceed us, they trounce us.
And where they don’t, it’s amazing how fast they are improving. Especially given that year to year, biological human capabilities are at a relative standstill.
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EDIT: I just tried the above test. The result was wonderful whimsical prose and references, that made sense at a very basic level, that a Supreme Court of 8 year olds would likely enjoy, especially if served along with some Dr. Seuss art! In about 10-15 seconds.
Viewed as a solution to an extremely complex constraint problem, that is simply amazing. And far beyond human capabilities on this dimension.