#Self-Consistency & Tree-of-Thought¶

Two ways to make reasoning more reliable by exploring multiple reasoning paths.

Self-Consistency¶

A single chain-of-thought can take a wrong turn. Self-consistency samples many independent reasoning paths and takes a majority vote on the final answer.

Same CoT prompt, temperature ≈ 0.7, run N times
   Path 1 → 28
   Path 2 → 28
   Path 3 → 31   ← outlier
   Path 4 → 28
Majority answer → 28

Higher accuracy on math/logic than a single sample
Cost scales with N (typically 5–20 samples)
Works because correct reasoning tends to converge; errors are diverse and scattered

Tree-of-Thought (ToT)¶

Generalises CoT into a search: at each step the model proposes several candidate next steps, evaluates them, and explores the most promising branches (with backtracking).

            Problem
           /   |   \
        idea1 idea2 idea3      ← generate candidates
          |     ✗     |        ← evaluate / prune
        step  (dead)  step
          |           |
        ...         solution

Good for problems where early commitment is costly: puzzles, planning, complex code design. More expensive and orchestration-heavy than self-consistency.

Practical Decision Guide¶

Need	Technique	Relative cost
Better answer on a hard, single-answer problem	Self-consistency (majority vote)	N×
Exploration with backtracking over a search space	Tree-of-Thought	High
Cheap reasoning boost	Plain chain-of-thought	1×

Implementation Sketch (Self-Consistency)¶

6 lines

1const answers = [];
2for (let i = 0; i < 7; i++) {
3  const r = await llm({ prompt: cotPrompt, temperature: 0.7 });
4  answers.push(extractAnswer(r));
5}
6const final = mode(answers); // most frequent

Rule of thumb: Reach for self-consistency when an answer is verifiable-but-hard and accuracy matters more than cost.

Self-Consistency¶

A single chain-of-thought can take a wrong turn. Self-consistency samples many independent reasoning paths and takes a majority vote on the final answer.

Same CoT prompt, temperature ≈ 0.7, run N times Path 1 → 28 Path 2 → 28 Path 3 → 31 ← outlier Path 4 → 28 Majority answer → 28

Higher accuracy on math/logic than a single sample

Cost scales with N (typically 5–20 samples)

Works because correct reasoning tends to converge; errors are diverse and scattered

Tree-of-Thought (ToT)¶

Generalises CoT into a search: at each step the model proposes several candidate next steps, evaluates them, and explores the most promising branches (with backtracking).

Good for problems where early commitment is costly: puzzles, planning, complex code design. More expensive and orchestration-heavy than self-consistency.

Need

Technique

Relative cost

Better answer on a hard, single-answer problem

Self-consistency (majority vote)

N×

Exploration with backtracking over a search space

Tree-of-Thought

High

Cheap reasoning boost

Plain chain-of-thought

1×

Implementation Sketch (Self-Consistency)¶

6 lines

1const answers = [];
2for (let i = 0; i < 7; i++) {
3  const r = await llm({ prompt: cotPrompt, temperature: 0.7 });
4  answers.push(extractAnswer(r));
5}
6const final = mode(answers); // most frequent

Rule of thumb: Reach for self-consistency when an answer is verifiable-but-hard and accuracy matters more than cost.