mlsanityData to 14 Oct 2026

On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective

arXiv 2605.21260 ↗First posted 20 May 2026cs.LGcited by 0

On the map: LLM reasoning → Prompting and chain-of-thought reasoning

Abstract (arXiv)

We develop a learning-theoretic framework for understanding Chain of Thought (CoT). We model CoT as the interaction between an answer map and a chain rule that generates intermediate questions autoregressively, and define the reasoning risk of a hypothesis under this interaction. Our first result is a tight canonical decomposition of this risk into two terms with opposing roles: an oracle-trajectory risk (OTR), which captures the benefit of CoT and reduces to a target-domain risk in a domain adaptation problem, and a trajectory-mismatch risk (TMR), which captures the cost of CoT through error accumulation along mismatched reasoning trajectories. We then show that this cost is unavoidable without structure: if any one of the loss, the hypothesis answer map, or the chain rule lacks stability, the TMR can be arbitrarily large even when the OTR is zero and the hypothesis is uniformly close to the ground truth. Conversely, under stability, we prove a tight upper bound on the TMR governed by an exact amplification factor that identifies bounded, linear, and exponential error-growth regimes. Together, these results give a precise theory of when CoT helps, when it hurts, and what controls the transition between the two.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning. Builds on 17 of its 119 references that are in the map. First posted on arXiv 20 May 2026.

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17 of 119 references.

Closest ancestors · 3

Same direction, newest first

  1. 2025Reasoning Models Don't Always Say What They Think8 May
  2. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models12 Mar
  3. 2023Why Can Large Language Models Generate Correct Chain-of-Thoughts?20 Oct

Other references · 14

  1. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
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  3. 2025OpenAI GPT-5 System Cardcited by 989
  4. 2021Show Your Work: Scratchpads for Intermediate Computation with Language Modelscited by 886
  5. 2023Gemini: A Family of Highly Capable Multimodal Modelscited by 872
  6. 2025Multimodal Chain-of-Thought Reasoning: A Comprehensive Surveycited by 182
  7. 2025Scaling Latent Reasoning via Looped Language Modelscited by 165
  8. 2025Implicit Reasoning in Large Language Models: A Comprehensive Surveycited by 43
  9. 2025A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Lawcited by 19
  10. 2025Not All Thoughts are Generated Equal: Efficient LLM Reasoning via Multi-Turn Reinforcement Learningcited by 16
  11. 2025Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfallscited by 7
  12. 2026Beyond the Black Box: A Survey on the Theory and Mechanism of Large Language Modelscited by 6
2 more
  1. 2025Evolution of meta's llama models and parameter-efficient fine-tuning of large language models: a surveycited by 5
  2. 2026Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov Statescited by 1

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  1. 2026When does Chain-of-Thought Help: A Markovian Perspective
  2. 2025Bounds of Chain-of-Thought Robustness: Reasoning Steps, Embed Norms, and Beyond
  3. 2026Beyond the Commitment Boundary: Probing Epiphenomenal Chain-of-Thought in Large Reasoning Models
  4. 2025Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillation
  5. 2026Structural Chain-of-Thought: Reasoning with Executable Computational Graphs
  6. 2026Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning
  7. 2025From Reasoning to Super-Intelligence: A Search-Theoretic Perspective
  8. 2026Rethinking Dense Sequential Chains: Reasoning Language Models Can Extract Answers from Sparse, Order-Shuffling Chain-of-Thoughts