atomic-decompositionlisted

# 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 C