Legacy Concept Lab

Chain-of-Thought Prompting

Dramatically improves reasoning performance—math, logic, coding

Concept 75 of 100Scaling & AlignmentPhase 11

#75CoTScaling & Alignment

key equationP(answer | question, reasoning)

Phase 11: Frontier research & scalingConcept 75 of 100

Why It Matters for Modern Models

What is still poorly explained in textbooks and papers:

CoT gives the model "scratchpad" space for intermediate computation
The reasoning doesn't need to be human-readable—it just needs to help the model
Self-consistency leverages diversity: different reasoning paths vote on the answer

If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.

Key Equation

P(answer | question, reasoning)

Chain-of-Thought: Prompt model to show reasoning steps:

P(answer | question) \to P(answer | question, reasoning)

Self-Consistency: Sample multiple reasoning paths, majority vote:

answer^* = \arg\max_a \sum_{i=1}^N \mathbf{1}[a_i = a]

where $a_i \sim P(a | q, r_i)$ with reasoning path $r_i$ .

Decomposition: Break complex problem into sub-problems:

P(y | x) = \prod_{t=1}^T P(y_t | y_{<t}, x)

Wei et al.2022NeurIPS

Wang et al.2023ICLR

Explore this concept from different angles — like a mathematician would.