It can do basic arithmetic because it's fed millions or billions of synthetic calculations as training data.

Quick!

What's the next top-k tokens after each of these?

"999 + 999 = "

"999.0 + 999.0 = "

"999 * 2 = "

"999 * (3-2) = "

Mathematically identical. But as a token sequence, not so much.

Modern models will of course have very similar next-token distributions across all of these. But not identical!

Now add a few digits and you quickly land in territory whose synthetic training data is much sparser.

Code has determinism and runs in milliseconds. It's the better tool for the job.

But if you add a few digits, the model writes a python or js program to calculate, it doesn't use next-token to guess.

(BTW the last one was meant to be (3-1).)

I think it might get the last one of those questions correct.

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