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

arXiv:2510.03527v2 Announce Type: replace Abstract: 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.

Abstract: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.

Computation and Language (cs.CL)

arXiv:2510.03527 [cs.CL]

(or arXiv:2510.03527v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2510.03527 Focus to learn more arXiv-issued DOI via DataCite

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

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