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atomic-decomposition

atomic-decomposition

github.com/lingzhi227Development4401.6k installsUpdated 35w ago
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About atomic-decomposition

A research skill that breaks an idea, paper, or method into traceable concepts and connects their mathematical formulations to code implementations. It also compiles the results into a structured knowledge base and checks for gaps.

Key features

  1. 01Atomic concept breakdown
  2. 02Paper and formula surveys
  3. 03Code implementation surveys
  4. 04Structured knowledge-base compilation
  5. 05Formula-to-code consistency checks

Use cases

  1. 01Decomposing a proposed research method
  2. 02Tracing formulas to implementations
  3. 03Finding theory or implementation gaps

Install

Copy the command and run it in a terminal.

$npx skills add https://github.com/lingzhi227/agent-research-skills --skill atomic-decomposition

After installing, type/atomic-decompositionin Claude Code to confirm it loaded.

Bundled filesreferences/decomposition-prompts.md

Details

From the project README

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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