title: Atom of Thoughts for Markov LLM Test-Time Scaling
summary: Large Language Models (LLMs) achieve superior performance through
  training-time scaling, and test-time scaling further enhances their
  capabilities by conducting effective reasoning during inference. However, as
  the scale of reasoning increases, existing test-time scaling methods suffer
  from accumulated historical information, which not only wastes computational
  resources but also interferes with effective reasoning. To address this issue,
  we observe that complex reasoning progress is often achieved by solving a
  sequence of independent subquestions, each being self-contained and verifiable.
  These subquestions are essentially atomic questions, relying primarily on their
  current state rather than accumulated history, similar to the memoryless
  transitions in a Markov process. Based on this observation, we propose Atom of
  Thoughts (AoT), where each state transition in the reasoning process consists
  of decomposing the current question into a dependency-based directed acyclic
  graph and contracting its subquestions, forming a new atomic question state.
  This iterative decomposition-contraction process continues until reaching
  directly solvable atomic questions, naturally realizing Markov transitions
  between question states. Furthermore, these atomic questions can be seamlessly
  integrated into existing test-time scaling methods, enabling AoT to serve as a
  plug-in enhancement for improving reasoning capabilities. Experiments across
  six benchmarks demonstrate the effectiveness of AoT both as a standalone
  framework and a plug-in enhancement. Notably, on HotpotQA, when applied to
  gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and
  DeepSeek-R1 by 10.6%. The code will be available at
  https://github.com/qixucen/atom.
paper_authors._id: 67b5c4ed85107d20148ae710
paper_authors.name: Fengwei Teng
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-02-19T11:49:34.612Z
paper_authors._id: 6402e8fb06c715b93407442d
paper_authors.avatarUrl: /avatars/12b67f0632be5a53b56d8a68586a7f98.svg
paper_authors.fullname: Fengwei Teng
paper_authors.type: user
paper_authors.user: leavendough
paper_authors._id: 67b5c4ed85107d20148ae711
paper_authors.name: Zhaoyang Yu
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-02-19T14:43:14.422Z
paper_authors._id: 640dc84b474aa6f89554d518
paper_authors.avatarUrl: /avatars/64f47f76d97c5e91b7ab8380bcada61c.svg
paper_authors.fullname: Zhaoyang Yu
paper_authors.type: user
paper_authors.user: MoshiQAQ
paper_authors._id: 67b5c4ed85107d20148ae712
paper_authors.name: Quan Shi
paper_authors._id: 67b5c4ed85107d20148ae713
paper_authors.name: Jiayi Zhang
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-02-19T14:43:54.773Z
paper_authors._id: 66071c8b013a0afdf40fbfd1
paper_authors.avatarUrl: /avatars/683e4ba5991059110631759a5975eacc.svg
paper_authors.fullname: JiaYi Zhang
paper_authors.type: user
paper_authors.user: Bbedd
paper_authors._id: 67b5c4ed85107d20148ae714
paper_authors.name: Chenglin Wu
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-04-08T06:58:28.754Z
paper_authors._id: 64252594a4f3051f54dd4355
paper_authors.avatarUrl: /avatars/c1f982b9b6be2956f6b6558be70d9ec3.svg
paper_authors.fullname: Wu
paper_authors.type: user
paper_authors.user: alexanderwu
paper_authors._id: 67b5c4ed85107d20148ae715
paper_authors.name: Yuyu Luo
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-04-08T06:58:25.567Z
paper_authors._id: 67efa8a2ed790a2e999dc216
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/0S4lQCJX61uCF8EkSLMkk.png
paper_authors.fullname: Yuyu Luo
paper_authors.type: user
paper_authors.user: luoyuyu
paper_title: Atom of Thoughts for Markov LLM Test-Time Scaling
paper_summary: Large Language Models (LLMs) achieve superior performance through
  training-time scaling, and test-time scaling further enhances their
  capabilities by conducting effective reasoning during inference. However, as
  the scale of reasoning increases, existing test-time scaling methods suffer
  from accumulated historical information, which not only wastes computational
  resources but also interferes with effective reasoning. To address this issue,
  we observe that complex reasoning progress is often achieved by solving a
  sequence of independent subquestions, each being self-contained and verifiable.
  These subquestions are essentially atomic questions, relying primarily on their
  current state rather than accumulated history, similar to the memoryless
  transitions in a Markov process. Based on this observation, we propose Atom of
  Thoughts (AoT), where each state transition in the reasoning process consists
  of decomposing the current question into a dependency-based directed acyclic
  graph and contracting its subquestions, forming a new atomic question state.
  This iterative decomposition-contraction process continues until reaching
  directly solvable atomic questions, naturally realizing Markov transitions
  between question states. Furthermore, these atomic questions can be seamlessly
  integrated into existing test-time scaling methods, enabling AoT to serve as a
  plug-in enhancement for improving reasoning capabilities. Experiments across
  six benchmarks demonstrate the effectiveness of AoT both as a standalone
  framework and a plug-in enhancement. Notably, on HotpotQA, when applied to
  gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and
  DeepSeek-R1 by 10.6%. The code will be available at
  https://github.com/qixucen/atom.
paper_ai_summary: Atom of Thoughts (AoT) enhances reasoning capabilities in Large Language Models by decomposing complex questions into independent subquestions, leading to improved performance and efficiency.
paper_ai_keywords: Large Language Models test-time scaling reasoning subquestions Markov process dependency-based directed acyclic graph atomic questions