Chain-of-Thought Prompting

01 · 写满过程，就一定真的会做吗01 · Does showing work prove the work is sound

一份答案写了五行推理，另一份只写结果；如果五行里有错但最后数字碰巧正确，应该相信哪一个证据？One answer shows five lines of reasoning; another gives only a result. If a step is wrong but the final number happens to be right, what should you trust?

02切换直接答与分步答，并列答案、token 与独立验算Switch Direct and Step-by-step Answers; Compare Output, Tokens, and Independent Verification

答案 ≠ 推理忠实性answer ≠ reasoning faithfulness

状态 AMetric A

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状态 BMetric B

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状态 CMetric C

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所有概率、命中率、得分与输出均为固定种子的教学模拟，不代表真实模型。拖回主变量即可复核结论。All probabilities, hit rates, scores, and outputs are fixed-seed teaching simulations, not real model output. Move the main variable back to verify the conclusion.

03把刚才的变化拆成 4 个零件Break the Change into Four Parts

Chain-of-Thought Prompting

PROMPT

回答要求Answer instruction

直接答或要求展示分步文本。Request either a direct answer or visible steps.

RATIONALE

中间推理Intermediate reasoning

可检查，但也可能包含自洽外观下的错误。It is inspectable, yet can contain errors beneath a coherent surface.

ANSWER

最终答案Final answer

正确结果不反向证明每一步正确。A correct result does not prove every step was correct.

VERIFY

独立验算Independent check

用外部规则或工具复核关键计算。External rules or tools verify the critical calculation.

04最小机制：主交互能逐项验证Minimal Mechanism: Verify Each Link in the Interaction

MECHANISM

trust = final_answer_check ∧ independent_reasoning_check

主交互让答案固定为 102，再单独改变中间算式；验算器因此能显示“答案 PASS、推理 FAIL”的组合。The interaction keeps the final answer at 102 while changing an intermediate equation, exposing the combination answer PASS, reasoning FAIL.

选择表达Choose style直接或分步direct or step by step

产生文本Generate text答案 + 可选推理answer + optional rationale

独立校验Verify independently不把流畅当正确do not equate fluency with truth

05让错误推理碰巧得到正确答案Make Incorrect Reasoning Land on the Correct Answer

主动制造失败Create a failure

边界实验Boundary experiment

把 7 × 6 错写成 40，却在结尾抄回 102；如果只看最终答案，这条错误推理会漏过。Miswrite 7 × 6 as 40, then copy 102 into the final line. Checking only the answer would miss the faulty reasoning.

尚未执行。先在主交互中观察正常机制。Not run yet. Observe the normal mechanism in the main interaction first.

✗ 写出思维链就证明模型真实这样想。A chain of thought proves how the model truly reasoned.→ ✓ 可见推理是输出文本，不等同内部因果过程。Visible reasoning is output text, not the model's internal causal process.

✗ 最终答案正确，推理就一定正确。A correct answer guarantees correct reasoning.→ ✓ 错误步骤也可能碰巧落在正确结果。Faulty steps can still land on the correct result.

✗ 分步答总比直接答更省。Step-by-step is always cheaper than direct answers.→ ✓ 它通常消耗更多 token，应按任务与验算需求选择。It usually costs more tokens and should be chosen by task and verification need.

06 · 一句话带走06 · One line to keep

思维链提示能提供可检查的分步文本，但更长不等于更真；最终答案与中间推理必须分开验算。Chain-of-thought prompting can expose inspectable steps, but longer is not truer. Verify the final answer and intermediate reasoning separately.