Atom of Thoughts for Markov LLM Test-Time Scaling
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.
67b5c4ed85107d20148ae710
Fengwei Teng
claimed_verified
2025-02-19T11:49:34.612Z
6402e8fb06c715b93407442d
/avatars/12b67f0632be5a53b56d8a68586a7f98.svg
Fengwei Teng
user
leavendough
67b5c4ed85107d20148ae711
Zhaoyang Yu
admin_assigned
2025-02-19T14:43:14.422Z
640dc84b474aa6f89554d518
/avatars/9fcee1023ed5c6cddb3c342e19f18295.svg
Zhaoyang Yu
user
MoshiQAQ
67b5c4ed85107d20148ae712
Quan Shi
67b5c4ed85107d20148ae713
Jiayi Zhang
admin_assigned
2025-02-19T14:43:54.773Z
66071c8b013a0afdf40fbfd1
/avatars/683e4ba5991059110631759a5975eacc.svg
JiaYi Zhang
user
Bbedd
67b5c4ed85107d20148ae714
Chenglin Wu
claimed_verified
2025-04-08T06:58:28.754Z
64252594a4f3051f54dd4355
/avatars/c1f982b9b6be2956f6b6558be70d9ec3.svg
Wu
user
alexanderwu
67b5c4ed85107d20148ae715
Yuyu Luo
claimed_verified
2025-04-08T06:58:25.567Z
67efa8a2ed790a2e999dc216
https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/0S4lQCJX61uCF8EkSLMkk.png
Yuyu Luo
user
luoyuyu
Atom of Thoughts for Markov LLM Test-Time Scaling
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.
Atom of Thoughts (AoT) enhances reasoning capabilities in Large Language Models by decomposing complex questions into independent subquestions, leading to improved performance and efficiency.
Large Language Models test-time scaling reasoning subquestions Markov process dependency-based directed acyclic graph atomic questions