mlsanityData to 14 Oct 2026

Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning

arXiv 2501.15602 ↗First posted 26 Jan 2025cs.AI cs.CLcited by 36

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model's internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 22 of its 42 references that are in the map. First posted on arXiv 26 Jan 2025.

Builds on

22 of 42 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems12 Dec
  2. 2024Enhancing LLM Reasoning with Reward-guided Tree Search18 Nov
  3. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  4. 2024Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models1 Aug
  5. 2023Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training29 Sep

Other references · 17

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2020Scaling Laws for Neural Language Modelscited by 6,586
  4. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  5. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  6. 2023Let's Verify Step by Stepcited by 3,789
  7. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  8. 2023Scaling Relationship on Learning Mathematical Reasoning with Large Language Modelscited by 427
  9. 2024ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Searchcited by 344
  10. 2022Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thoughtcited by 337
  11. 2024Skywork-Reward: Bag of Tricks for Reward Modeling in LLMscited by 327
  12. 2024The pitfalls of next-token predictioncited by 160
5 more
  1. 2024HelpSteer2-Preference: Complementing Ratings with Preferencescited by 130
  2. 2024MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Timecited by 41
  3. 2019BottleSum: Unsupervised and Self-supervised Sentence Summarization using the Information Bottleneck Principlecited by 39
  4. 2024Understanding Chain-of-Thought in LLMs through Information Theorycited by 37
  5. 2024Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspectivecited by 15

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 18; 2026: 18.

36 papers.

Sort:

By area:

  1. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 384
  2. 2025Multimodal Chain-of-Thought Reasoning: A Comprehensive Surveycited by 182
  3. 2025Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoningcited by 51
  4. 2025Information Gain-based Policy Optimization: A Simple and Effective Approach for Multi-Turn Search Agentscited by 48
  5. 2025Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lenscited by 34
  6. 2026Understanding Agent Scaling in LLM-Based Multi-Agent Systems via Diversitycited by 29
  7. 2025A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Lawcited by 19
  8. 2025Explainable Chain-of-Thought Reasoning: An Empirical Analysis on State-Aware Reasoning Dynamicscited by 16
  9. 2025CTRLS: Chain-of-Thought Reasoning via Latent State-Transitioncited by 14
  10. 2026InT: Self-Proposed Interventions Enable Credit Assignment in LLM Reasoningcited by 14
  11. 2025CoAT: Chain-of-Associated-Thoughts Framework for Enhancing Large Language Models Reasoningcited by 12
  12. 2025Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoningcited by 10
24 more
  1. 2026Mitigating Overthinking in Large Reasoning Language Models via Reasoning Path Deviation Monitoringcited by 6
  2. 2025From Chaos to Order: The Atomic Reasoner Framework for Fine-grained Reasoning in Large Language Modelscited by 5
  3. 2025Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theorycited by 5
  4. 2026Streaming Hallucination Detection in Long Chain-of-Thought Reasoningcited by 5
  5. 2025Token Signature: Predicting Chain-of-Thought Gains with Token Decoding Feature in Large Language Modelscited by 4
  6. 2025A Stitch in Time Saves Nine: Proactive Self-Refinement for Language Modelscited by 4
  7. 2025Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thoughtcited by 4
  8. 2025ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimizationcited by 3
  9. 2025Diffuse Thinking: Exploring Diffusion Language Models as Efficient Thought Proposers for Reasoningcited by 3
  10. 2026Reliable Chain-of-Thought via Prefix Consistencycited by 3
  11. 2026From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Modelscited by 2
  12. 2026When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitionscited by 2
  13. 2026The Diminishing Returns of Early-Exit Decoding in Modern LLMscited by 1
  14. 2026From Inertia to Objectivity: Improving Deep Research Agents with Noise Isolationcited by 1
  15. 2026It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectoriescited by 1
  16. 2025Stepwise Reasoning Checkpoint Analysis: A Test Time Scaling Method to Enhance LLMs' Reasoningcited by 0
  17. 2026Latent Reward Steering: An Adaptive Inference-Time Framework that Implicitly Promotes Cognitive Behaviors in Reasoning LLMscited by 0
  18. 2026Test-Time Scaling in Multimodal Foundation Models: A Comprehensive Survey of Generation and Reasoningcited by 0
  19. 2026Contextual Information Policy Optimization for Search Agentscited by 0
  20. 2026ORDDAR: Observation-Driven Reasoning for Distortion-Resilient Decision, Action, and Cognitive Recoverycited by 0
  21. 2026GUT: Quantifying and Optimizing the Reasoning Uncertainty of LLMs via Graph Complexitycited by 0
  22. 2026GRUET: Quantifying Uncertainty of Agentic Reasoning-and-Acting Processescited by 0
  23. 2026Interpreting Reasoning of Large Language Models via Partial Information Decompositioncited by 0
  24. 2026PHRBench: A Behavioral Evaluation of Post-Hallucination Reasoning in LLMscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026When More Thinking Hurts: Overthinking in LLM Test-Time Compute Scaling
  2. 2025Double-Checker: Enhancing Reasoning of Slow-Thinking LLMs via Self-Critical Fine-Tuning
  3. 2025Test-Time Scaling in Reasoning Models Is Not Effective for Knowledge-Intensive Tasks Yet
  4. 2025Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs
  5. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning
  6. 2025Harnessing the Reasoning Economy: A Survey of Efficient Reasoning for Large Language Models
  7. 2025Fast, Slow, and Tool-augmented Thinking for LLMs: A Review
  8. 2026To Think or Not To Think, That is The Question for Large Reasoning Models in Theory of Mind Tasks