# Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoning

arXiv: https://arxiv.org/abs/2506.09853 · HTML: https://mlsanity.com/paper/2506.09853/

## 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.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 46)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Active Prompting with Chain-of-Thought for Large Language Models](https://mlsanity.com/paper/2302.12246/) (2023)
- [The Impact of Reasoning Step Length on Large Language Models](https://mlsanity.com/paper/2401.04925/) (2024)
- [The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Tasks](https://mlsanity.com/paper/2502.08235/) (2025)
- [Graph Chain-of-Thought: Augmenting Large Language Models by Reasoning on Graphs](https://mlsanity.com/paper/2404.07103/) (2024)
- [C3oT: Generating Shorter Chain-of-Thought without Compromising Effectiveness](https://mlsanity.com/paper/2412.11664/) (2024)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [Effectively Controlling Reasoning Models through Thinking Intervention](https://mlsanity.com/paper/2503.24370/) (2025)
- [A Comparative Study on Reasoning Patterns of OpenAI's o1 Model](https://mlsanity.com/paper/2410.13639/) (2024)

## Built on by (most cited first, 17 of 17)

- [Can Aha Moments Be Fake? Towards Quantifying Decorative and True Thinking in Chain-of-Thought](https://mlsanity.com/paper/2510.24941/) (2025)
- [Dynamics Within Latent Chain-of-Thought: An Empirical Study of Causal Structure](https://mlsanity.com/paper/2602.08783/) (2026)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [iReasoner: Trajectory-Aware Intrinsic Reasoning Supervision for Self-Evolving Large Multimodal Models](https://mlsanity.com/paper/2601.05877/) (2026)
- [CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2507.15698/) (2025)
- [FACT-E: Causality-Inspired Evaluation for Trustworthy Chain-of-Thought Reasoning](https://mlsanity.com/paper/2604.10693/) (2026)
- [Interpreting Agentic Systems: Beyond Model Explanations to System-Level Accountability](https://mlsanity.com/paper/2601.17168/) (2026)
- [ToolGate: Token-Efficient Pre-Call Control for Tool-Augmented Vision-Language Agents](https://mlsanity.com/paper/2606.03054/) (2026)
- [Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesis](https://mlsanity.com/paper/2604.14121/) (2026)
- [Systematic Optimization of Open Source Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2509.07238/) (2025)
- [Foundation Models for Medical Imaging: Status, Challenges, and Directions](https://mlsanity.com/paper/2602.15913/) (2026)
- [CAMO: An Agentic Framework for Automated Causal Discovery from Micro Behaviors to Macro Emergence in LLM Agent Simulations](https://mlsanity.com/paper/2604.14691/) (2026)
- [Reasoning4Sciences: Bridging Reasoning Language Models to All Scientific Branches](https://mlsanity.com/paper/2606.01145/) (2026)
- [Beyond Sufficiency: Time Series Explanation with Counterfactual Necessity](https://mlsanity.com/paper/2607.21573/) (2026)
- [Externalized CPDAG Summaries Improve LLM Causal Deduction](https://mlsanity.com/paper/2609.31071/) (2026)
- [Where MLLMs Fail and Why: Causal Task Decomposition for Capability Failure Diagnosis](https://mlsanity.com/paper/2609.38851/) (2026)
- [Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models](https://mlsanity.com/paper/2610.05472/) (2026)

## 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.