Self-Consistency Improves Chain of Thought Reasoning in Language Models

Wang et al., ICLR 2023 · arXiv:2203.11171 — SAMPLE PRESENTATION (course template)

STML 2026 · exemplar deck by the instructor

1 · Contribution in one sentence

This paper solves the problem that one greedy reasoning chain fails on problems the model can actually solve — by sampling many diverse reasoning paths and taking the majority answer.

• No training, no new model — a decoding strategy swap at inference time.
• Works on top of chain-of-thought prompting as-is.

[1 min] Template slide 1 = the whole paper in one sentence, in the “solves X by Y” shape. Say it, don’t read it. Everything after this slide is evidence for this sentence.

2 · Problem & motivation

Chain-of-thought prompting made models show multi-step reasoning — but decoding stayed greedy: the model commits to a single chain, token by token.

• One early wrong step poisons everything after it; the final answer is hostage to a single path.
• Yet a complex problem usually admits several different valid ways to reach its one correct answer — greedy decoding throws that diversity away.
• Prior fixes (trained verifiers, re-rankers) require extra training; nothing exploited the model’s own sampling.

[2 min] Template slide 2 = why now + what prior work couldn’t do. The motivation is stated as a mechanism gap (greedy = one path), not as “accuracy was low.”

3 · Core mechanism

flowchart LR
    Q["question<br/>+ CoT prompt"] --> S1["path 1 (sampled, T>0):<br/>...so 8 + 10 = 18"]
    Q --> S2["path 2 (sampled):<br/>...therefore 26"]
    Q --> S3["path 3 (sampled):<br/>...which gives 18"]
    S1 --> E["extract final answers:<br/>18 · 26 · 18"]
    S2 --> E
    S3 --> E
    E --> V["majority vote<br/>(marginalize over paths)"]
    V --> A["answer: 18"]

1. Sample N reasoning chains with temperature > 0 (instead of one greedy chain).
2. Extract only the final answer from each chain — the chain text itself is discarded.
3. Vote: return the most frequent answer. Formally, this marginalizes out the reasoning paths.

Wrong paths tend to scatter across different wrong answers; correct paths agree.

[5 min] Template slide 3 = the mechanism, on a figure you drew yourself (this diagram is original — pasting the paper’s Figure 1 is not allowed). Walk the three paths out loud; the 18/26/18 example carries the whole idea. The one term worth saying precisely: “marginalizing out reasoning paths” — voting is a sum over latent paths.

4 · One key result

GSM8K (grade-school math): +17.9% absolute over CoT with greedy decoding — from sampling alone, no training.

Benchmark	Gain over greedy CoT
GSM8K	+17.9%
AQuA	+12.2%
SVAMP	+11.0%
StrategyQA	+6.4%
ARC-challenge	+3.9%

What this proves: a large share of CoT’s errors are decoding accidents, not capability limits — the model already contained the correct reasoning; greedy decoding just failed to surface it.

[3 min] Template slide 4 = ONE result and what it proves — not a tour of every table. The claim sentence at the bottom is the slide’s job; the table is only support. Numbers are from the paper’s abstract (verified).

5 · Weakest assumption

The vote needs answers that can be compared for equality.

• Works when the final answer is short and discrete (a number, a multiple-choice option). For open-ended outputs — a proof, an essay, code — “most consistent answer” has no exact-match definition.
• Also assumes errors are diverse while truth converges: under a systematic bias (e.g. a consistent unit-conversion mistake), the majority converges on the same wrong answer, confidently.
• And the cost is honest: N samples = N× the inference cost of one chain.

[3 min] Template slide 5 = the critique you chose yourself — the rubric scores whether you found the load-bearing assumption, not whether you listed many small caveats. Ranked here: comparability (structural), error diversity (statistical), cost (practical).

6 · Connection

• Successors relax slide 5’s limits: Tree of Thoughts (search instead of independent samples), trained verifiers / LLM judges (vote replaced by scoring — usable for open-ended outputs).
• In this course: you implement exactly this loop in the W3 lab (N=5 vote, watching accuracy vs. N); the N× cost returns in W11 inference economics as the compute-optimal question — when is N samples of a small model better than 1 call to a large one?

[1 min] Template slide 6 = one link forward (literature) + one link home (your work). Then slides off — cold questions are answered at the whiteboard.