# Divide-and-Conquer Meets Consensus: Unleashing the Power of Functions in Code Generation

arXiv: https://arxiv.org/abs/2405.20092 · HTML: https://mlsanity.com/paper/2405.20092/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 65 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 47)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [CodeBERT: A Pre-Trained Model for Programming and Natural Languages](https://mlsanity.com/paper/2002.08155/) (2020)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [CodeT5: Identifier-aware Unified Pre-trained Encoder-Decoder Models for Code Understanding and Generation](https://mlsanity.com/paper/2109.00859/) (2021)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [CodeXGLUE: A Machine Learning Benchmark Dataset for Code Understanding and Generation](https://mlsanity.com/paper/2102.04664/) (2021)
- [CodeSearchNet Challenge: Evaluating the State of Semantic Code Search](https://mlsanity.com/paper/1909.09436/) (2019)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)

## Built on by (most cited first, 19 of 19)

- [CodeTree: Agent-guided Tree Search for Code Generation with Large Language Models](https://mlsanity.com/paper/2411.04329/) (2024)
- [Internet of Agents: Fundamentals, Applications, and Challenges](https://mlsanity.com/paper/2505.07176/) (2025)
- [MAPRO: Recasting Multi-Agent Prompt Optimization as Maximum a Posteriori Inference](https://mlsanity.com/paper/2510.07475/) (2025)
- [StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion](https://mlsanity.com/paper/2508.04440/) (2025)
- [Reasoning-as-Logic-Units: Scaling Test-Time Reasoning in Large Language Models Through Logic Unit Alignment](https://mlsanity.com/paper/2502.07803/) (2025)
- [DISC: Dynamic Decomposition Improves LLM Inference Scaling](https://mlsanity.com/paper/2502.16706/) (2025)
- [SIGMA: Refining Large Language Model Reasoning via Sibling-Guided Monte Carlo Augmentation](https://mlsanity.com/paper/2506.06470/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Program Synthesis via Test-Time Transduction](https://mlsanity.com/paper/2509.17393/) (2025)
- [Agint: Agentic Graph Compilation for Software Engineering Agents](https://mlsanity.com/paper/2511.19635/) (2025)
- [Falsification, Not Exposure: An Internally Preregistered Placebo-Controlled Decomposition of Self-Repair Feedback in Frozen Small Code Models](https://mlsanity.com/paper/2606.31511/) (2026)
- [A Theoretical Analysis of Test-Driven Code Generation](https://mlsanity.com/paper/2602.06098/) (2026)
- [PaT: Planning-after-Trial for Efficient Test-Time Code Generation](https://mlsanity.com/paper/2605.07248/) (2026)
- [Majority Voting for Code Generation](https://mlsanity.com/paper/2604.15618/) (2026)
- [Harness as a Language: A Minimalist Agent Framework With Maximal Expressivity](https://mlsanity.com/paper/2609.26891/) (2026)
- [DecompRL: Solving Harder Problems by Learning Modular Code Generation](https://mlsanity.com/paper/2607.02390/) (2026)
- [MineValiCoder: Reliable Code Generation with Test Case Quality Mining and Bipartite Graph-Based Mutual Validation](https://mlsanity.com/paper/2607.22471/) (2026)
- [Entropy-Regularized Rank-Masked Policy Optimization for Test-Time Reinforcement Learning in Code Generation](https://mlsanity.com/paper/2609.09135/) (2026)
- [Confidence-Gated Transductive Test Generation for Code Reranking](https://mlsanity.com/paper/2609.12489/) (2026)

## Abstract (arXiv)

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.