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When the model guesses and the guess is off, something has to say by how much. For cats and dogs that was easy. The answer was right or it was not.
Text does not work that way, because the model never puts forward a single word.
Give it The dog and ask what comes next. It does not answer barked. It spreads its confidence across every word it knows: a good share on barked, a good share on ran, less on slept, almost none on saucepan, and some sliver on each of the hundred thousand others. Its guess is not a word. It is a shape.
Now the sentence turns out to continue The dog barked. Wrongness is a measurement rather than a verdict, so the question is how much confidence the model had put on barked before it found out. A large share, and the error is small. Almost none, and the error is large.
One number, produced fresh at every step of every stretch of text.
That number is what all of it is built to make smaller. Every chip, every megawatt, every month of training exists to make the model less surprised by the next word.
Working out which weights to blame for that number, and by how much, is backpropagation, doing here exactly what it did when the first small network learned.