Atomic Thought (AoT)

Decomposes problems into independent atomic units that can be reasoned about without historical context dependency.

Core Mechanism

Apply a two-phase cycle until the problem is directly solvable:

1. Decomposition: Break the current question into a dependency graph of sub-questions
2. Contraction: Solve independent sub-questions, then contract answers into a simplified atomic question

Process

1. Identify the question's component parts
2. Map dependencies: which sub-questions require answers from others?
3. Solve independent (leaf) sub-questions first—each answer must be self-contained
4. Contract: Reformulate the original question using obtained answers
5. Repeat until directly answerable

Key Principles

• Markov property: Each atomic state contains everything needed to solve it
• No context accumulation: Solved sub-problems contract into the question, not into growing context
• Independence first: Prioritize sub-questions that don't depend on others

When to Apply

• Multi-hop factual queries requiring information from multiple sources
• Research tasks with distinct knowledge areas
• Problems where irrelevant context degrades reasoning quality
• Tasks parallelizable across independent sub-problems

Example Pattern

Original: "What is the GDP difference between the birthplace of the inventor of the telephone and the country where pizza originated?"

Decomposition:
├── Q1: Who invented the telephone? [independent]
├── Q2: Where was [Q1 answer] born? [depends on Q1]
├── Q3: Where did pizza originate? [independent]
├── Q4: What is GDP of [Q2 answer]? [depends on Q2]
└── Q5: What is GDP of [Q3 answer]? [depends on Q3]

Solve Q1, Q3 → Contract → Solve Q2, Q5 → Contract → Compute difference

Anti-Patterns

• Using for simple single-hop questions (overhead not justified)
• Maintaining full reasoning history across atomic units
• Creating dependencies where none exist