Same apples word problem, run two ways. STANDARD prompting makes the model jump straight to "The answer is 27" — wrong, marked with a gray cross. CHAIN-OF-THOUGHT prompting adds "Let us think step by step", and the reasoning appears one step at a time — 23 minus 20 equals 3, plus 6 equals 9 — landing on the right answer, 9, marked with an amber check. The only change is whether the model is given room to write its steps; that room is compute spent at answer-time.

Room to think

Same question, run two ways. A single forward pass guesses the answer in one leap. Give the model room to write the steps and it composes the answer instead.

pretraining

predict the next word

post-training

follow + prefer

answer-time

spend compute thinking

prompt

The cafeteria had 23 apples. They used 20 to make lunch and bought 6 more. How many apples do they have?
Let us think step by step.
model

output

The model never changed — only whether it was allowed to write its steps. One leap is a guess; the steps let it carry 23 - 20 = 3 forward into 3 + 6 = 9. More compute at answer-time → better answers on hard problems.