title: Fractured Chain-of-Thought Reasoning
summary: Inference-time scaling techniques have significantly bolstered the reasoning
  capabilities of large language models (LLMs) by harnessing additional
  computational effort at inference without retraining. Similarly,
  Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy
  by generating rich intermediate reasoning trajectories, but these approaches
  incur substantial token costs that impede their deployment in latency-sensitive
  settings. In this work, we first show that truncated CoT, which stops reasoning
  before completion and directly generates the final answer, often matches full
  CoT sampling while using dramatically fewer tokens. Building on this insight,
  we introduce Fractured Sampling, a unified inference-time strategy that
  interpolates between full CoT and solution-only sampling along three orthogonal
  axes: (1) the number of reasoning trajectories, (2) the number of final
  solutions per trajectory, and (3) the depth at which reasoning traces are
  truncated. Through extensive experiments on five diverse reasoning benchmarks
  and several model scales, we demonstrate that Fractured Sampling consistently
  achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling
  gains in Pass@k versus token budget. Our analysis reveals how to allocate
  computation across these dimensions to maximize performance, paving the way for
  more efficient and scalable LLM reasoning.
paper_authors._id: 682c12290f622b7afc1fc98f
paper_authors.name: Baohao Liao
paper_authors.status: admin_assigned
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paper_authors.fullname: Baohao Liao
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paper_authors._id: 682c12290f622b7afc1fc990
paper_authors.name: Hanze Dong
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paper_authors.fullname: Hanze Dong
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paper_authors.user: hendrydong
paper_authors._id: 682c12290f622b7afc1fc991
paper_authors.name: Yuhui Xu
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paper_authors.fullname: Yuhui Xu
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paper_authors.user: yuhuixu
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paper_authors.name: Doyen Sahoo
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paper_authors.fullname: Doyen
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paper_authors.user: doyensahoo
paper_authors._id: 682c12290f622b7afc1fc993
paper_authors.name: Christof Monz
paper_authors._id: 682c12290f622b7afc1fc994
paper_authors.name: Junnan Li
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-05-20T08:34:18.715Z
paper_authors._id: 61f9d3b54ac99e8a1bae85f4
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paper_authors.fullname: JunnanLi
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paper_authors.user: JunnanLi
paper_authors._id: 682c12290f622b7afc1fc995
paper_authors.name: Caiming Xiong
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-05-20T08:34:27.628Z
paper_authors._id: 649dbcc4e0fff1ed099dc80a
paper_authors.avatarUrl: /avatars/c87c273ca628dbcddccbf1ee19b2ce33.svg
paper_authors.fullname: Caiming Xiong
paper_authors.type: user
paper_authors.user: cxiong
paper_title: Fractured Chain-of-Thought Reasoning
paper_summary: Inference-time scaling techniques have significantly bolstered the reasoning
  capabilities of large language models (LLMs) by harnessing additional
  computational effort at inference without retraining. Similarly,
  Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy
  by generating rich intermediate reasoning trajectories, but these approaches
  incur substantial token costs that impede their deployment in latency-sensitive
  settings. In this work, we first show that truncated CoT, which stops reasoning
  before completion and directly generates the final answer, often matches full
  CoT sampling while using dramatically fewer tokens. Building on this insight,
  we introduce Fractured Sampling, a unified inference-time strategy that
  interpolates between full CoT and solution-only sampling along three orthogonal
  axes: (1) the number of reasoning trajectories, (2) the number of final
  solutions per trajectory, and (3) the depth at which reasoning traces are
  truncated. Through extensive experiments on five diverse reasoning benchmarks
  and several model scales, we demonstrate that Fractured Sampling consistently
  achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling
  gains in Pass@k versus token budget. Our analysis reveals how to allocate
  computation across these dimensions to maximize performance, paving the way for
  more efficient and scalable LLM reasoning.
paper_ai_summary: Fractured Sampling optimizes inference in large language models by balancing token usage and accuracy through truncated reasoning trajectories.
paper_ai_keywords: inference-time scaling large language models Chain-of-Thought (CoT) Long CoT truncated CoT Fractured Sampling reasoning trajectories final solutions reasoning traces Pass@k token budget