# Cumulative Reasoning with Large Language Models

arXiv: https://arxiv.org/abs/2308.04371 · HTML: https://mlsanity.com/paper/2308.04371/

## 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.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 55)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Model](https://mlsanity.com/paper/2201.11990/) (2022)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)

## Built on by (most cited first, 30 of 94)

- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [Personal LLM Agents: Insights and Survey about the Capability, Efficiency and Security](https://mlsanity.com/paper/2401.05459/) (2024)
- [DyVal: Dynamic Evaluation of Large Language Models for Reasoning Tasks](https://mlsanity.com/paper/2309.17167/) (2023)
- [Cognitive Mirage: A Review of Hallucinations in Large Language Models](https://mlsanity.com/paper/2309.06794/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [StateFlow: Enhancing LLM Task-Solving through State-Driven Workflows](https://mlsanity.com/paper/2403.11322/) (2024)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Large Language Model-Powered Smart Contract Vulnerability Detection: New Perspectives](https://mlsanity.com/paper/2310.01152/) (2023)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [TreeRPO: Tree Relative Policy Optimization](https://mlsanity.com/paper/2506.05183/) (2025)
- [Budget-Aware Tool Use Enables Effective Agent Scaling](https://mlsanity.com/paper/2511.17006/) (2025)
- [DetermLR: Augmenting LLM-based Logical Reasoning from Indeterminacy to Determinacy](https://mlsanity.com/paper/2310.18659/) (2023)
- [Semantic-Aware Logical Reasoning via a Semiotic Framework](https://mlsanity.com/paper/2509.24765/) (2025)
- [Achieving >97% on GSM8K: Deeply Understanding the Problems Makes LLMs Better Solvers for Math Word Problems](https://mlsanity.com/paper/2404.14963/) (2024)
- [Internet of Agents: Fundamentals, Applications, and Challenges](https://mlsanity.com/paper/2505.07176/) (2025)
- [Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning](https://mlsanity.com/paper/2601.02902/) (2026)
- [Deductive Beam Search: Decoding Deducible Rationale for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2401.17686/) (2024)
- [Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratch](https://mlsanity.com/paper/2410.18693/) (2024)
- [Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models](https://mlsanity.com/paper/2409.17539/) (2024)
- [LLMDFA: Analyzing Dataflow in Code with Large Language Models](https://mlsanity.com/paper/2402.10754/) (2024)
- [Boosting of Thoughts: Trial-and-Error Problem Solving with Large Language Models](https://mlsanity.com/paper/2402.11140/) (2024)
- [Group Think: Multiple Concurrent Reasoning Agents Collaborating at Token Level Granularity](https://mlsanity.com/paper/2505.11107/) (2025)
- [Holistic Evaluation of GPT-4V for Biomedical Imaging](https://mlsanity.com/paper/2312.05256/) (2023)
- [Divide-and-Conquer Meets Consensus: Unleashing the Power of Functions in Code Generation](https://mlsanity.com/paper/2405.20092/) (2024)
- [Ranked Voting based Self-Consistency of Large Language Models](https://mlsanity.com/paper/2505.10772/) (2025)
- [Imitation Learning for Multi-turn LM Agents via On-policy Expert Corrections](https://mlsanity.com/paper/2512.14895/) (2025)

## 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%.