mlsanityData to 14 Oct 2026

Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoning

arXiv 2506.09853 ↗First posted 11 Jun 2025cs.CL cs.AI math.STcited by 17

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

Abstract (arXiv)

Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the generated intermediate inference steps comprehensively cover and substantiate the final conclusion; and (2) Necessity, which identifies the inference steps that are truly indispensable for the soundness of the resulting answer. We propose a causal framework that characterizes CoT reasoning through the dual lenses of sufficiency and necessity. Incorporating causal Probability of Sufficiency and Necessity allows us not only to determine which steps are logically sufficient or necessary to the prediction outcome, but also to quantify their actual influence on the final reasoning outcome under different intervention scenarios, thereby enabling the automated addition of missing steps and the pruning of redundant ones. Extensive experimental results on various mathematical and commonsense reasoning benchmarks confirm substantial improvements in reasoning efficiency and reduced token usage without sacrificing accuracy. Our work provides a promising direction for improving LLM reasoning performance and cost-effectiveness.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning. Builds on 46 of its 78 references that are in the map. First posted on arXiv 11 Jun 2025.

Builds on

46 of 78 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025Chain of Draft: Thinking Faster by Writing Less25 Feb
  2. 2025Stepwise Perplexity-Guided Refinement for Efficient Chain-of-Thought Reasoning in Large Language Models18 Feb
  3. 2025Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought8 Jan
  4. 2024Training Large Language Models to Reason in a Continuous Latent Space9 Dec
  5. 2024Chain-of-Thought in Large Language Models: Decoding, Projection, and Activation5 Dec
  6. 2024Understanding Chain-of-Thought in LLMs through Information Theory18 Nov
  7. 2024Markov Chain of Thought for Efficient Mathematical Reasoning23 Oct
  8. 2024To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning18 Sep
  9. 2024Self-Harmonized Chain of Thought6 Sep
  10. 2024Break the Chain: Large Language Models Can be Shortcut Reasoners4 Jun
  11. 2024The Impact of Reasoning Step Length on Large Language Models10 Jan
  12. 2023Active Prompting with Chain-of-Thought for Large Language Models23 Feb
1 more
  1. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Models21 Mar

Other references · 33

  1. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  2. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  3. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  4. 2018CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledgecited by 1,822
  5. 2024OpenAI o1 System Cardcited by 1,244
  6. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,210
  7. 2024DeepSeek-V3 Technical Reportcited by 811
  8. 2024Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMscited by 570
  9. 2024LLaVA-CoT: Let Vision Language Models Reason Step-by-Stepcited by 454
  10. 2025O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruningcited by 279
  11. 2024Token-Budget-Aware LLM Reasoningcited by 247
  12. 2024Compressed Chain of Thought: Efficient Reasoning Through Dense Representationscited by 201
21 more
  1. 2025ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoningcited by 201
  2. 2025Reasoning Models Can Be Effective Without Thinkingcited by 187
  3. 2025CoT-Valve: Length-Compressible Chain-of-Thought Tuningcited by 169
  4. 2025The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Taskscited by 152
  5. 2024Graph Chain-of-Thought: Augmenting Large Language Models by Reasoning on Graphscited by 119
  6. 2024C3oT: Generating Shorter Chain-of-Thought without Compromising Effectivenesscited by 119
  7. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoningcited by 119
  8. 2024Fast Best-of-N Decoding via Speculative Rejectioncited by 112
  9. 2025Self-Training Elicits Concise Reasoning in Large Language Modelscited by 99
  10. 2025Effectively Controlling Reasoning Models through Thinking Interventioncited by 65
  11. 2024A Comparative Study on Reasoning Patterns of OpenAI's o1 Modelcited by 63
  12. 2025Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Mathcited by 44
  13. 2025Trust Me, I'm Wrong: LLMs Hallucinate with Certainty Despite Knowing the Answercited by 27
  14. 2025Thought Manipulation: External Thought Can Be Efficient for Large Reasoning Modelscited by 23
  15. 2024Rational Metareasoning for Large Language Modelscited by 20
  16. 2024Increasing the LLM Accuracy for Question Answering: Ontologies to the Rescue!cited by 18
  17. 2024DOTS: Learning to Reason Dynamically in LLMs via Optimal Reasoning Trajectories Searchcited by 17
  18. 2024Reasoning Elicitation in Language Models via Counterfactual Feedbackcited by 14
  19. 2024Mitigating Copy Bias in In-Context Learning through Neuron Pruningcited by 11
  20. 2024OpenAI-o1 AB Testing: Does the o1 model really do good reasoning in math problem solving?cited by 4
  21. 2024Refining Answer Distributions for Improved Large Language Model Reasoningcited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 14.

17 papers.

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  1. 2025Can Aha Moments Be Fake? Towards Quantifying Decorative and True Thinking in Chain-of-Thoughtcited by 15
  2. 2026Dynamics Within Latent Chain-of-Thought: An Empirical Study of Causal Structurecited by 11
  3. 2026Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Modelscited by 8
  4. 2026iReasoner: Trajectory-Aware Intrinsic Reasoning Supervision for Self-Evolving Large Multimodal Modelscited by 7
  5. 2025CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoningcited by 5
  6. 2026FACT-E: Causality-Inspired Evaluation for Trustworthy Chain-of-Thought Reasoningcited by 4
  7. 2026Interpreting Agentic Systems: Beyond Model Explanations to System-Level Accountabilitycited by 2
  8. 2026ToolGate: Token-Efficient Pre-Call Control for Tool-Augmented Vision-Language Agentscited by 2
  9. 2026Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesiscited by 1
  10. 2025Systematic Optimization of Open Source Large Language Models for Mathematical Reasoningcited by 0
  11. 2026Foundation Models for Medical Imaging: Status, Challenges, and Directionscited by 0
  12. 2026CAMO: An Agentic Framework for Automated Causal Discovery from Micro Behaviors to Macro Emergence in LLM Agent Simulationscited by 0
5 more
  1. 2026Reasoning4Sciences: Bridging Reasoning Language Models to All Scientific Branchescited by 0
  2. 2026Beyond Sufficiency: Time Series Explanation with Counterfactual Necessitycited by 0
  3. 2026Externalized CPDAG Summaries Improve LLM Causal Deductioncited by 0
  4. 2026Where MLLMs Fail and Why: Causal Task Decomposition for Capability Failure Diagnosiscited by 0
  5. 2026Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters
  2. 2026Valid ne Necessary: Diagnosing Latent Inefficiency in Chain-of-Thought
  3. 2025Unveiling and Causalizing CoT: A Causal Pespective
  4. 2026Fragile Thoughts: How Large Language Models Handle Chain-of-Thought Perturbations
  5. 2025Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens
  6. 2024Chain-of-Thought Reasoning Without Prompting
  7. 2026Does Verbose Chain-of-Thought Really Help? In-Distribution Evidence that Content, Not Length, Matters
  8. 2026When Chain-of-Thought Helps and When It Hurts: An Empirical Investigation of the Serial-Depth Bottleneck in LLM Reasoning