atomic-decomposition

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Atomic Decomposition

原子分解

Decompose research ideas into atomic concepts with math formula <-> code implementation mapping.

将研究思想分解为具备数学公式<->代码实现映射的原子概念。

Input

输入

```
$0
```
— Research idea, paper, or method description

```
$0
```
— 研究思路、论文或方法描述

References

参考文献

Decomposition prompts and workflow:

~/.claude/skills/atomic-decomposition/references/decomposition-prompts.md

分解提示词与工作流：

~/.claude/skills/atomic-decomposition/references/decomposition-prompts.md

Workflow (from AI-Researcher Survey Agent)

工作流（来自AI-Researcher Survey Agent）

Step 1: Break Down into Atomic Definitions

步骤1：拆解为原子定义

Analyze the research idea and decompose into atomic, self-contained concepts:

Each atom should be a single concept
Must have clear mathematical foundations
Must be implementable in code
Must be traceable to specific papers

分析研究思想并将其分解为原子化、独立的概念：

每个原子单元应对应单个概念
必须具备清晰的数学基础
必须可通过代码实现
必须可追溯至特定论文

Step 2: For Each Atomic Definition

步骤2：针对每个原子定义

A. Paper Survey (Math Formula)

A. 论文调研（数学公式）

Search papers for the mathematical formulation
Extract the exact LaTeX formula
Note assumptions and constraints
Record reference papers

检索论文以获取数学表达式
提取精确的LaTeX公式
记录假设条件与约束
记录参考文献论文

B. Code Survey (Implementation)

B. 代码调研（实现方案）

Search codebases for implementations
Extract the corresponding code
Note implementation details and variations
Record reference repositories

检索代码库以获取实现示例
提取对应的代码
记录实现细节与变体
记录参考代码仓库

C. Create Knowledge Entry

C. 创建知识条目

json

{
  "definition": "Kernelized Gumbel-Softmax Operator",
  "math_formula": "Z = \\text{softmax}((\\log \\pi + g) / \\tau), g \\sim \\text{Gumbel}(0,1)",
  "code_implementation": "def gumbel_softmax(logits, tau=1.0): ...",
  "reference_papers": ["Paper Title 1"],
  "reference_codebases": ["github_user/repo_name"],
  "assumptions": ["Differentiable relaxation of discrete sampling"],
  "connections": ["Used in Component X of the proposed method"]
}