# Chain of Thought

> Academic breakdown of latent reasoning and token probability manipulation.

- Skill: `j4flmao/chain-of-thought` (Agent Skill)
- Install (CLI): `npx skillmds@latest add j4flmao/chain-of-thought`
- Raw SKILL.md: https://api.skillmd.com/api/skills/j4flmao/chain-of-thought/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: j4flmao (https://skillmd.com/u/j4flmao)
- Updated: 2026-09-21
- Page: https://skillmd.com/skills/j4flmao/chain-of-thought

---

# Chain of Thought (CoT) Prompting Mechanics

## Latent Reasoning Elicitation
Chain of Thought (CoT) acts as a mechanism to externalize latent reasoning steps that the transformer model otherwise attempts to compress into a single forward pass. By coercing the model to generate intermediate tokens, the effective computation allocated to the problem scales linearly with the sequence length (compute-per-token scaling). This breaks complex, multi-hop logical dependencies into localized, attention-manageable segments.

## Token Probability Manipulation
Autoregressive language models generate tokens based on the joint probability distribution conditioned on prior tokens.
In standard zero-shot generation: $P(y|"x)$ where $x$ is the prompt and $y$ is the answer.
In CoT: $P(y"|x, z_1, z_2, ..., z_n)$ where $z_i$ are reasoning steps.
By generating $z_i$, the attention mechanism shifts probability mass toward logically consistent completions. The presence of structural reasoning markers (e.g., "Therefore", "First") strongly biases the top-k token logits towards coherent, logically sound outputs, effectively acting as an explicit regularizer on the distribution space.

```mermaid
%%{init: {"theme": "default", "flowchart": {"useMaxWidth": true}}}%%
flowchart TD
    Prompt["Input Prompt"] -->|"Encode()"| Embeddings
    
    subgraph TransformerTransformerBlock ["Transformer Block<br><br><br>"]
        Embeddings --> Attention["Self-Attention"]
        Attention --> FFN["Feed Forward Network"]
        FFN --> Logits["Token Logits"]
    end
    
    subgraph CoTChainofThought ["Chain of Thought<br><br><br>"]
        Logits -->|"Sample()"| Token_Z["Intermediate Reasoning Token (z_i)"]
        Token_Z -->|"Append()"| Context["Updated Context"]
        Context -->|"AutoRegressive()"| Attention
    end
    
    Token_Z -->|"Finalize()"| Answer["Final Answer (y)"]
```