atom-of-thought

When facing a complex problem, use this approach:

Step 1: Direct Assessment

Attempt to solve the original problem directly to establish a baseline understanding.

Step 2: Atomic Decomposition

Discover sub-questions in four passes — don't target a count:

Pass 1 — Generate freely: List every conceptually separable question embedded in the problem. Don't filter yet.

Pass 2 — Atomize: For each question, ask "does this embed multiple independent questions?" If yes, split it. Keep splitting until each one is indivisible.

Pass 3 — Mark dependencies: A dependency is only information that must come from a previous sub-question's answer — not from the problem statement itself. Don't mark known things as dependencies.

Pass 4 — Completeness & prune:

• Completeness: "If I resolved every question on this list, would the original problem be fully solved?" If not, add what's missing.
• Prune: Remove any sub-question whose answer is already explicit in the problem statement.

Decomposition Template:

Main Problem: [Original question/task]

Atomic Sub-questions:
Q1: [Question] — DEPENDENCIES: none
Q2: [Question] — DEPENDENCIES: none
...
Qn: [Question] — DEPENDENCIES: [Q1, Q3]

Completeness check: Resolving all Qs above fully answers the original problem? [Yes / No — if No, add missing atoms]

Dependency Graph: [Visualize relationships]

Step 3: Parallel Resolution

Solve all independent atomic questions first, in parallel:

Independent Resolutions:
Q1: [Question] → [Answer + Evidence]
Q2: [Question] → [Answer + Evidence]
...

Step 4: Dependency Resolution

Solve dependent questions using resolved atoms as known conditions:

Dependent Resolutions:
Q3 (needs Q1, Q2): Given [Q1 answer] and [Q2 answer], [modified question] → [Answer]
...

Step 5: Contraction & Integration

Reformulate the original problem using all resolved atoms as known conditions:

Contracted Problem: Given [all resolved atoms], [simplified original question]
Final Answer: [Integrated solution]

Step 6: Ensemble Validation

Compare direct solution vs. AoT solution:

• Which approach provides more confidence?
• Are results consistent?
• Final decision with reasoning

Meta-Guidelines:

• Markov Property: Each step depends only on current state, not history
• Iterative Depth: If contracted problem still complex, repeat AoT process
• Atomic Validation: Ensure each atom is truly independent or has clear dependencies
• Efficiency Focus: Avoid redundant reasoning paths

This framework transforms complex reasoning into manageable atomic operations while maintaining logical dependencies.