SECURITY REVIEW
Not yet assessed
Review the original instructions and requested permissions before installing.
No security review is available for this catalog entry yet.
Research / AGENT SKILL
atomic-decomposition
0
Break research ideas into self-contained concepts and map mathematical formulas to code implementations.
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.
Understand the trade-offs.
SKILL QUALITY
Not yet assessed
How clearly the skill guides your agent, how complete its workflow is, and how you can check the outcome.
No quality assessment is available for this catalog entry yet.
The full skill.
Original instructions from the publisher’s SKILL.md
# 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
```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"]
}
```
### 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
## Related Skills
- Upstream: [research-planning](../research-planning/), [idea-generation](../idea-generation/)
- Downstream: [experiment-code](../experiment-code/), [algorithm-design](../algorithm-design/)
- See also: [math-reasoning](../math-reasoning/)