mlsanityData to 14 Oct 2026

Cumulative Reasoning with Large Language Models

arXiv 2308.04371 ↗First posted 8 Aug 2023cs.AIcited by 94

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

Recent advancements in large language models (LLMs) have shown remarkable progress, yet their ability to solve complex problems remains limited. In this work, we introduce Cumulative Reasoning (CR), a structured framework that enhances LLM problem-solving by emulating human-like iterative and cumulative thought processes. CR orchestrates LLMs in three distinct roles: Proposer, Verifier(s), and Reporter, to systematically decompose tasks, generate and validate intermediate reasoning steps, and compose them into a solution by building a dynamic Directed Acyclic Graph (DAG) of verified propositions. This approach substantially enhances problem-solving capabilities. We demonstrate CR's advantage through several complex reasoning tasks: it outperforms existing methods in logical inference tasks with up to a 9.3% improvement, achieving 98.04% accuracy on the curated FOLIO wiki dataset. In the Game of 24, it achieves 98% accuracy, marking a 24% improvement over previous methods. In solving MATH problems, CR achieves a 4.2% increase from previous methods and a 43% relative improvement in the most challenging level 5 problems. When incorporating a code environment with CR, we further harness LLMs' reasoning capabilities and outperform the Program of Thought (PoT) method by 38.8%.

Key facts. Cited by 94 papers in the map (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 55 of its 140 references that are in the map. First posted on arXiv 8 Aug 2023.

Builds on

55 of 140 references.

Closest ancestors · 8

Same direction, newest first

  1. 2023Improving Factuality and Reasoning in Language Models through Multiagent Debate23 May
  2. 2023PaLM 2 Technical Report17 May
  3. 2023LLaMA: Open and Efficient Foundation Language Models27 Feb
  4. 2022PAL: Program-aided Language Models18 Nov
  5. 2022FOLIO: Natural Language Reasoning with First-Order Logic2 Sep
  6. 2022Faithful Reasoning Using Large Language Models30 Aug
  7. 2022Making Large Language Models Better Reasoners with Step-Aware Verifier6 Jun
  8. 2021Show Your Work: Scratchpads for Intermediate Computation with Language Models30 Nov

Other references · 47

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2023GPT-4 Technical Reportcited by 18,396
  4. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,599
  5. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  6. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2022PaLM: Scaling Language Modeling with Pathwayscited by 5,326
  9. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,276
  10. 2023Let's Verify Step by Stepcited by 3,789
  11. 2022OPT: Open Pre-trained Transformer Language Modelscited by 3,512
  12. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,442
35 more
  1. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,211
  2. 2022Training Compute-Optimal Large Language Modelscited by 3,019
  3. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,998
  4. 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,407
  5. 2022LaMDA: Language Models for Dialog Applicationscited by 1,220
  6. 2021Scaling Language Models: Methods, Analysis & Insights from Training Gophercited by 1,202
  7. 2022Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Taskscited by 1,076
  8. 2022Solving math word problems with process- and outcome-based feedbackcited by 901
  9. 2021GLaM: Efficient Scaling of Language Models with Mixture-of-Expertscited by 897
  10. 2021Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigmcited by 606
  11. 2022Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Modelcited by 559
  12. 2022Decomposed Prompting: A Modular Approach for Solving Complex Taskscited by 558
  13. 2023LeanDojo: Theorem Proving with Retrieval-Augmented Language Modelscited by 427
  14. 2022Complexity-Based Prompting for Multi-Step Reasoningcited by 388
  15. 2020ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Languagecited by 324
  16. 2023Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspectivecited by 294
  17. 2022Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofscited by 291
  18. 2023Faithful Chain-of-Thought Reasoningcited by 288
  19. 2021AI Chains: Transparent and Controllable Human-AI Interaction by Chaining Large Language Model Promptscited by 268
  20. 2023Large Language Model Guided Tree-of-Thoughtcited by 221
  21. 2019KagNet: Knowledge-Aware Graph Networks for Commonsense Reasoningcited by 216
  22. 2020Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learningcited by 216
  23. 2023Progressive-Hint Prompting Improves Reasoning in Large Language Modelscited by 147
  24. 2020Scalable Multi-Hop Relational Reasoning for Knowledge-Aware Question Answeringcited by 122
  25. 2020INFOTABS: Inference on Tables as Semi-structured Datacited by 86
  26. 2021When Can Models Learn From Explanations? A Formal Framework for Understanding the Roles of Explanation Datacited by 75
  27. 2019Cognitive Graph for Multi-Hop Reading Comprehension at Scalecited by 65
  28. 2017Thinking Fast and Slow: Optimization Decomposition Across Timescalescited by 60
  29. 2018Knowledgeable Reader: Enhancing Cloze-Style Reading Comprehension with External Commonsense Knowledgecited by 48
  30. 2018Improving Natural Language Inference Using External Knowledge in the Science Questions Domaincited by 48
  31. 2018Commonsense for Generative Multi-Hop Question Answering Taskscited by 48
  32. 2022SeqZero: Few-shot Compositional Semantic Parsing with Sequential Prompts and Zero-shot Modelscited by 38
  33. 2021Refining Language Models with Compositional Explanationscited by 27
  34. 2018Exploiting Explicit Paths for Multi-hop Reading Comprehensioncited by 16
  35. 2022Realistic Data Augmentation Framework for Enhancing Tabular Reasoningcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 17; 2024: 33; 2025: 26; 2026: 18.

94 papers.

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  1. 2025s1: Simple test-time scalingcited by 1,341
  2. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  3. 2025R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalizationcited by 370
  4. 2024Personal LLM Agents: Insights and Survey about the Capability, Efficiency and Securitycited by 260
  5. 2023DyVal: Dynamic Evaluation of Large Language Models for Reasoning Taskscited by 101
  6. 2023Cognitive Mirage: A Review of Hallucinations in Large Language Modelscited by 84
  7. 2024Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solvingcited by 84
  8. 2024StateFlow: Enhancing LLM Task-Solving through State-Driven Workflowscited by 65
  9. 2024Demystifying Chains, Trees, and Graphs of Thoughtscited by 63
  10. 2024Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoningcited by 58
  11. 2025Empowering LLMs with Logical Reasoning: A Comprehensive Surveycited by 51
  12. 2023Large Language Model-Powered Smart Contract Vulnerability Detection: New Perspectivescited by 48
38 more
  1. 2023Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiencycited by 46
  2. 2025TreeRPO: Tree Relative Policy Optimizationcited by 46
  3. 2025Budget-Aware Tool Use Enables Effective Agent Scalingcited by 44
  4. 2023DetermLR: Augmenting LLM-based Logical Reasoning from Indeterminacy to Determinacycited by 34
  5. 2025Semantic-Aware Logical Reasoning via a Semiotic Frameworkcited by 32
  6. 2024Achieving >97% on GSM8K: Deeply Understanding the Problems Makes LLMs Better Solvers for Math Word Problemscited by 31
  7. 2025Internet of Agents: Fundamentals, Applications, and Challengescited by 31
  8. 2026Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoningcited by 25
  9. 2024Deductive Beam Search: Decoding Deducible Rationale for Chain-of-Thought Reasoningcited by 24
  10. 2024Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratchcited by 24
  11. 2024Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Modelscited by 23
  12. 2024LLMDFA: Analyzing Dataflow in Code with Large Language Modelscited by 22
  13. 2024Boosting of Thoughts: Trial-and-Error Problem Solving with Large Language Modelscited by 22
  14. 2025Group Think: Multiple Concurrent Reasoning Agents Collaborating at Token Level Granularitycited by 22
  15. 2023Holistic Evaluation of GPT-4V for Biomedical Imagingcited by 19
  16. 2024Divide-and-Conquer Meets Consensus: Unleashing the Power of Functions in Code Generationcited by 19
  17. 2025Ranked Voting based Self-Consistency of Large Language Modelscited by 19
  18. 2025Imitation Learning for Multi-turn LM Agents via On-policy Expert Correctionscited by 19
  19. 2026TSRBench: A Comprehensive Multi-task Multi-modal Time Series Reasoning Benchmark for Generalist Modelscited by 18
  20. 2024A Survey of Large Language Models on Generative Graph Analytics: Query, Learning, and Applicationscited by 17
  21. 2024Arithmetic Reasoning with LLM: Prolog Generation & Permutationcited by 17
  22. 2023Meta Prompting for AI Systemscited by 16
  23. 2024On the Diagram of Thoughtcited by 16
  24. 2023Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approachcited by 15
  25. 2023StrategyLLM: Large Language Models as Strategy Generators, Executors, Optimizers, and Evaluators for Problem Solvingcited by 13
  26. 2024Synergy-of-Thoughts: Eliciting Efficient Reasoning in Hybrid Language Modelscited by 13
  27. 2024SocraSynth: Multi-LLM Reasoning with Conditional Statisticscited by 13
  28. 2024How Can LLM Guide RL? A Value-Based Approachcited by 13
  29. 2024ArgMed-Agents: Explainable Clinical Decision Reasoning with LLM Disscusion via Argumentation Schemescited by 13
  30. 2025UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Modelscited by 13
  31. 2025Evolutionary Perspectives on the Evaluation of LLM-Based AI Agents: A Comprehensive Surveycited by 13
  32. 2025Problem-Solving Logic Guided Curriculum In-Context Learning for LLMs Complex Reasoningcited by 12
  33. 2025A Survey on Mathematical Reasoning and Optimization with Large Language Modelscited by 12
  34. 2025BMMR: A Large-Scale Bilingual Multimodal Multi-Discipline Reasoning Datasetcited by 12
  35. 2024A Theory for Length Generalization in Learning to Reasoncited by 11
  36. 2024Toward Adaptive Reasoning in Large Language Models with Thought Rollbackcited by 11
  37. 2025Unlocking the Power of Multi-Agent LLM for Reasoning: From Lazy Agents to Deliberationcited by 11
  38. 2025AutoTool: Dynamic Tool Selection and Integration for Agentic Reasoningcited by 11

50 most cited of 94 All 94 (JSON)

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  1. 2025Knowledge Augmented Complex Problem Solving with Large Language Models: A Survey
  2. 2025Advancing Reasoning in Large Language Models: Promising Methods and Approaches
  3. 2023GraphReason: Enhancing Reasoning Capabilities of Large Language Models through A Graph-Based Verification Approach
  4. 2024Multi-Step Reasoning with Large Language Models, a Survey
  5. 2025Computational Thinking Reasoning in Large Language Models
  6. 2025FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving
  7. 2024Divide-or-Conquer? Which Part Should You Distill Your LLM?
  8. 2025PEA: Enhancing LLM Performance on Computational-Reasoning Tasks