# Sample, Align, Synthesize: Graph-Based Response Synthesis with ConGrs

arXiv: https://arxiv.org/abs/2510.03527 · HTML: https://mlsanity.com/paper/2510.03527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 53 of its 75 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 30 of 53)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [How Language Model Hallucinations Can Snowball](https://mlsanity.com/paper/2305.13534/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [Factuality Enhanced Language Models for Open-Ended Text Generation](https://mlsanity.com/paper/2206.04624/) (2022)
- [Self-Evaluation Guided Beam Search for Reasoning](https://mlsanity.com/paper/2305.00633/) (2023)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)

## Abstract (arXiv)

Language models can be sampled multiple times to access the distribution underlying their responses, but existing methods cannot efficiently synthesize rich epistemic signals across different long-form responses. We introduce Consensus Graphs (ConGrs), a flexible DAG-based data structure that represents shared information, as well as semantic variation in a set of sampled LM responses to the same prompt. We construct ConGrs using a light-weight lexical sequence alignment algorithm from bioinformatics, supplemented by the targeted usage of a secondary LM judge. Further, we design task-dependent decoding methods to synthesize a single, final response from our ConGr data structure. Our experiments show that synthesizing responses from ConGrs improves factual precision on two biography generation tasks by up to 31% over an average response and reduces reliance on LM judges by more than 80% compared to other methods. We also use ConGrs for three refusal-based tasks requiring abstention on unanswerable queries and find that abstention rate is increased by up to 56%. We apply our approach to the MATH and AIME reasoning tasks and find an improvement over self-verification and majority vote baselines by up to 6 points of accuracy. We show that ConGrs provide a flexible method for capturing variation in LM responses and using the epistemic signals provided by response variation to synthesize more effective responses.