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Atomic decomposition

Skill dongzhigang13305312738-art/paper-skills/atomic-decomposition

📝 124 个 SCI/SSCI 论文写作 AI 技能合集：选题→文献综述→实验→图表→写作→润色→去AI痕迹→投稿，一个 paper-studio 总入口全流程调度。支持 Claude Code / WorkBuddy。

Install
npx -y skills add dongzhigang13305312738-art/paper-skills --skill atomic-decomposition

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What its author says it does

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Decompose research ideas into atomic, self-contained concepts with bidirectional math-code mapping. For each concept, extract the math formula from papers and find code implementations. Use for complex system papers requiring formal grounding.

SKILL.md

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Atomic Decomposition

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

Input

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

References

  • Decomposition prompts and workflow: ~/.claude/skills/atomic-decomposition/references/decomposition-prompts.md

Workflow (from AI-Researcher Survey Agent)

Step 1: Break Down into Atomic Definitions

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

Step 2: For Each Atomic Definition

A. Paper Survey (Math Formula)

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

B. Code Survey (Implementation)

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

C. Create Knowledge Entry

{
  "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"]
}

Step 3: Compile Knowledge Base

  • Merge all atomic definitions into a structured knowledge base
  • Verify consistency: every math formula has a code implementation
  • Verify completeness: every code module traces to a formal definition
  • Identify any gaps (formulas without code, or code without theory)

Rules

  • Each atomic definition must be specific enough to trace to concrete formulas and code
  • Do not skip or combine definitions — analyze each separately
  • If unsure about atomicity, err on the side of breaking down further
  • Document breakdown reasoning before analysis
  • Every mathematical concept in the paper must have verified code
  • Every code module must trace back to a formal mathematical definition

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