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What is Chain-of-Thought Reasoning?

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Engineering Notes · AI Systems

The model uses chain-of-thought reasoning, spending several seconds working before it answers.

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Overview

Chain-of-thought reasoning is an AI model working a problem in steps before it answers, instead of replying instantly. Writing the intermediate steps out makes it far more accurate on anything needing several stages, like math or logic. It is the technique behind the newer models that visibly pause to think.
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Overview

Chain-of-thought is the model working the problem out in steps instead of blurting an answer. Writing the steps gives it somewhere to put half-finished thinking, which makes it far better at math and logic. It is why the newer models sit there visibly thinking before they reply. 😎

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Detail

A model produces its answer one word at a time, and each word it writes is chosen based on the words already on the page. Those written words are therefore the only place it can park a half-finished result. Give it a problem with three stages, a price, then a discount, then tax, and demand the answer immediately: the very next thing it writes has to be the final number, so all three stages have to happen in that one move. Let it write the stages out instead, and the discounted price appears on the page as an actual number, which the tax stage can then read and use. The gain from that is large, and it is measured: the original 2022 research more than tripled a model's score on grade-school math problems, same model, only told to work step by step. Working step by step costs more, because every step is text the model must generate, so a reasoning answer burns several times the compute of a direct one and takes longer, which is why models that pause are priced higher. One caveat: the steps a model shows are not guaranteed to be its actual reasons, so a tidy chain can still end up somewhere wrong.
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Detail

Every word a model writes is picked using the words already sitting on the page, which makes that page its only memory. Ask for a straight answer and the next thing out has to be the final number, with the entire calculation crammed into that single move. Tell it to work out loud and the halfway numbers land on the page as real text, so the next step just reads them off. Split a restaurant bill four ways with tip on top: doing it in one shot is a guess, writing the subtotal down first makes the rest trivial. The 2022 research that kicked this off more than tripled a model's grade-school math score doing nothing but asking it to work step by step. Not free though, because every step is text it has to generate, so you pay several times the compute and sit there waiting, which is why the thinky models cost more per question. And do not fully trust the show, because the steps it displays are not guaranteed to be its real reasons, so a gorgeous chain can still march confidently off a cliff. 😎

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Analogy

A student doing long division entirely in their head versus on paper. Same student, same arithmetic, but the mental version collapses halfway because there is nowhere to park the half-finished numbers. On paper each step sits there waiting, so the next step only has to handle what is written in front of it. The paper is not making anyone smarter; it is giving the work somewhere to live.
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Analogy

Doing a big grocery total in your head at the register versus punching it into your phone. Same brain either way, but in your head the subtotal evaporates the second you start on tax. On the phone every number stays put while you work the next one. The phone did not teach you arithmetic; it just stopped you dropping things halfway through.
Deepest level reached.

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Formal definition — The same term, explained the usual way

Chain-of-thought reasoning refers to prompting or training a language model to generate intermediate reasoning steps before a final answer, materially improving performance on multi-step arithmetic, logical and symbolic tasks. Because each generated step conditions subsequent generation, the technique supplies working memory absent from direct answering; it increases token consumption and latency, and generated rationales are not reliably faithful accounts of the model's actual computation.

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